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31 produkter

Analysis and Optimization of Differential Systems
IFIP TC7 / WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10–14, 2002, Constanta, Romania
AvConstantin Varsan,Dan Tibam. fl.
E-bok
PDF, Engelska, 2013
1 427 kr
Läs direkt efter köp
Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: Ordinary and partial differential systems; Optimal control of deterministic and stochastic evolution equations;Control theory of Partial Differential Equations (PDE''s); Optimization methods in PDE''s with numerous applications to mechanics and physics; Inverse problems; Stability theory; Abstract optimization problems; Calculus of variations; Numerical treatment of solutions to differential equations and related optimization problems.
These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering.
This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002. Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT program.
Del 310 - Mathematics and Its Applications
Mathematical Methods in Optimization of Differential Systems
AvViorel Barbu
Inbunden, Engelska, 1994
559 kr
Skickas inom 10-15 vardagar
This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.
Del 441 - Mathematics and Its Applications
Partial Differential Equations and Boundary Value Problems
AvViorel Barbu
Inbunden, Engelska, 1998
1 111 kr
Skickas inom 10-15 vardagar
The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense.
Stabilization of Navier–Stokes Flows
AvViorel Barbu
Inbunden, Engelska, 2010
1 111 kr
Skickas inom 10-15 vardagar
Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still.Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Stabilization of Navier-Stokes Flows
AvViorel Barbu
E-bok
PDF, Engelska, 2010
1 413 kr
Läs direkt efter köp
Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still.Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Analysis and Optimization of Differential Systems
IFIP TC7 / WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10–14, 2002, Constanta, Romania
AvViorel Barbu,Irena Lasieckam. fl.
Inbunden, Engelska, 2003
1 111 kr
Skickas inom 10-15 vardagar
This text focuses on the qualitative aspects of deterministic and stochastic differential equations. Areas covered include: ordinary and partial differential systems; optimal control of deterministic and stochastic evolution equations; control theory of partial differential equations (PDE's); optimization methods in PDE's with numerous applications to mechanics and physics; inverse problems; stability theory; abstract optimization problems; calculus of variations; numerical treatment of solutions to differential equations and related optimization problems. These research fields are under very active development and the present volume should be of interest to students and researchers working in applied mathematics or in system engineering. This volume contains selected contributions presented during the International Working Conference on Analysis and Optimization of Differential Systems, which was sponsored by the International Federation for Information Processing (IFIP) and held in Constanta, Romania in September 2002.Among the aims of this conference was the creation of new international contacts and collaborations, taking advantage of the new developments in Eastern Europe, particularly in Romania. The conference benefited from the support of the European Union via the EURROMMAT programme.
Nonlinear Differential Equations of Monotone Types in Banach Spaces
AvViorel Barbu
Inbunden, Engelska, 2010
1 111 kr
Skickas inom 10-15 vardagar
In the last decades, functional methods played an increasing role in the qualita tive theory of partial differential equations. The spectral methods and theory of C 0 semigroups of linear operators as well as Leray-Schauder degree theory, ?xed point theorems, and theory of maximal monotone nonlinear operators are now essential functional tools for the treatment of linear and nonlinear boundary value problems associated with partial differential equations. An important step was the extension in the early seventies of the nonlinear dy namics of accretive (dissipative) type of the Hille-Yosida theory of C semigroups 0 of linear continuous operators. The main achievement was that the Cauchy problem associated with nonlinear m accretive operators in Banach spaces is well posed and the corresponding dynamic is expressed by the Peano exponential formula from ?nite dimensional theory. This fundamental result is the corner stone of the whole existence theory of nonlinear in?nite dynamics of dissipative type and its contri bution to the development of the modern theory of nonlinear partial differential equations cannot be underestimated.
Nonlinear Differential Equations of Monotone Types in Banach Spaces
AvViorel Barbu
E-bok
PDF, Engelska, 2010
1 413 kr
Läs direkt efter köp
Stabilization of Navier–Stokes Flows
AvViorel Barbu
Häftad, Engelska, 2013
1 111 kr
Skickas inom 10-15 vardagar
Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still.Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Nonlinear Differential Equations of Monotone Types in Banach Spaces
AvViorel Barbu
Häftad, Engelska, 2012
1 111 kr
Skickas inom 10-15 vardagar
In the last decades, functional methods played an increasing role in the qualita tive theory of partial differential equations. The spectral methods and theory of C 0 semigroups of linear operators as well as Leray-Schauder degree theory, ?xed point theorems, and theory of maximal monotone nonlinear operators are now essential functional tools for the treatment of linear and nonlinear boundary value problems associated with partial differential equations. An important step was the extension in the early seventies of the nonlinear dy namics of accretive (dissipative) type of the Hille-Yosida theory of C semigroups 0 of linear continuous operators. The main achievement was that the Cauchy problem associated with nonlinear m accretive operators in Banach spaces is well posed and the corresponding dynamic is expressed by the Peano exponential formula from ?nite dimensional theory. This fundamental result is the corner stone of the whole existence theory of nonlinear in?nite dynamics of dissipative type and its contri bution to the development of the modern theory of nonlinear partial differential equations cannot be underestimated.
Analysis and Optimization of Differential Systems : IFIP TC7 / WG7.2 International Working Conference on Analysis and Optimization of Differential Sys
AvViorel Barbu,Irena Lasiecka
Engelska, 2013
646 kr
Skickas inom 5-8 vardagar
Analysis and Optimization of Differential Systems
IFIP TC7 / WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10–14, 2002, Constanta, Romania
AvViorel Barbu,Irena Lasieckam. fl.
Häftad, Engelska, 2013
1 111 kr
Skickas inom 10-15 vardagar
Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations.
Del 90 - Progress in Nonlinear Differential Equations and Their Applications
Controllability and Stabilization of Parabolic Equations
AvViorel Barbu
Häftad, Engelska, 2018
1 111 kr
Skickas inom 10-15 vardagar
This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.
Del 2353 - Lecture Notes in Mathematics
Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
AvViorel Barbu,Michael Röckner
Häftad, Engelska, 2024
657 kr
Skickas inom 5-8 vardagar
This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions.The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.
Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
AvMichael Rockner,Viorel Barbu
E-bok
Engelska, 2024
868 kr
Läs direkt efter köp
This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions.
The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.
Del 2163 - Lecture Notes in Mathematics
Stochastic Porous Media Equations
AvViorel Barbu,Giuseppe Da Pratom. fl.
Häftad, Engelska, 2016
604 kr
Skickas inom 10-15 vardagar
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Stochastic Porous Media Equations
AvMichael Rockner,Giuseppe Da Pratom. fl.
E-bok
PDF, Engelska, 2016
789 kr
Läs direkt efter köp
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Differential Equations
AvViorel Barbu
Häftad, Engelska, 2016
388 kr
Skickas inom 10-15 vardagar
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Differential Equations
AvViorel Barbu
E-bok
PDF, Engelska, 2016
475 kr
Läs direkt efter köp
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Del 90 - Progress in Nonlinear Differential Equations and Their Applications
Controllability and Stabilization of Parabolic Equations
AvViorel Barbu
Inbunden, Engelska, 2018
1 526 kr
Skickas inom 10-15 vardagar
This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.
Controllability and Stabilization of Parabolic Equations
AvViorel Barbu
E-bok
Engelska, 2018
1 413 kr
Läs direkt efter köp
This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear differential equations, Controllability and Stabilization of Parabolic Equations is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.
Nonlinear semigroups and differential equations in Banach spaces
AvViorel Barbu
Häftad, Engelska, 1976
1 634 kr
Skickas inom 10-15 vardagar
This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa tions associated with nonlinear dissipative operators. The study of nonlinear semi groups resulted from the examination of nonlinear parabolic equations and from various nonlinear boundary value problems. The first work done by Y. Komura stimulated much further work and interest in this subject. Thus a series of studies was begun and then continued by T. Kato, M. G. Crandall, A. Pazy, H. Brezis and others, who made important con tributions to the development of the theory. The theory as developed below is a generalisation of the Hille-Yosida theory for one-parameter semigroups of linear operators and is a collection of diversified results unified more or less loosely by their methods of approach. This theory is also closely related to the theory of nonlinear monotone operators. Of course not all aspects of this theory could be covered in our expo sition, and many important contributions to the subject have been excluded for the sake of brevity. We have attempted to present the basic results to the reader and to orient him toward some of the applications. This book is intended to be self-contained. The reader is assumed to have only a basic knowledge of functional analysis, function theory and partial differential equations. Some of the necessary prerequisites for the reading of this 'book are summarized, with or without proof, in Chapter I.
Del 441 - Mathematics and Its Applications
Partial Differential Equations and Boundary Value Problems
AvViorel Barbu
Häftad, Engelska, 2010
1 092 kr
Skickas inom 10-15 vardagar
The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense.
Convexity and Optimization in Banach Spaces
AvViorel Barbu,Teodor Precupanu
Inbunden, Engelska, 2012
1 417 kr
Skickas inom 10-15 vardagar
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Convexity and Optimization in Banach Spaces
AvTeodor Precupanu,Viorel Barbu
E-bok
PDF, Engelska, 2012
1 728 kr
Läs direkt efter köp
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Del 310 - Mathematics and Its Applications
Mathematical Methods in Optimization of Differential Systems
AvViorel Barbu
Häftad, Engelska, 2012
549 kr
Skickas inom 10-15 vardagar
This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.
Mathematical Methods in Optimization of Differential Systems
AvViorel Barbu
E-bok
PDF, Engelska, 2012
712 kr
Läs direkt efter köp
This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.
Partial Differential Equations and Boundary Value Problems
AvViorel Barbu
E-bok
PDF, Engelska, 2013
1 427 kr
Läs direkt efter köp
The material of the present book has been used for graduate-level courses at the University of Ia~i during the past ten years. It is a revised version of a book which appeared in Romanian in 1993 with the Publishing House of the Romanian Academy. The book focuses on classical boundary value problems for the principal equations of mathematical physics: second order elliptic equations (the Poisson equations), heat equations and wave equations. The existence theory of second order elliptic boundary value problems was a great challenge for nineteenth century mathematics and its development was marked by two decisive steps. Undoubtedly, the first one was the Fredholm proof in 1900 of the existence of solutions to Dirichlet and Neumann problems, which represented a triumph of the classical theory of partial differential equations. The second step is due to S. 1. Sobolev (1937) who introduced the concept of weak solution in partial differential equations and inaugurated the modern theory of boundary value problems. The classical theory which is a product ofthe nineteenth century, is concerned with smooth (continuously differentiable) sollutions and its methods rely on classical analysis and in particular on potential theory. The modern theory concerns distributional (weak) solutions and relies on analysis of Sob ole v spaces and functional methods. The same distinction is valid for the boundary value problems associated with heat and wave equations. Both aspects of the theory are present in this book though it is not exhaustive in any sense.
Convexity and Optimization in Banach Spaces
AvViorel Barbu,Teodor Precupanu
Häftad, Engelska, 2014
1 417 kr
Skickas inom 10-15 vardagar
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
SEMIGROUP APPROACH TO NONLINEAR DIFFUSION EQUATIONS
AvViorel Barbu
Inbunden, Engelska, 2021
1 246 kr
Skickas inom 3-6 vardagar
This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.

Viorel Barbu – författare

Analysis and Optimization of Differential Systems

Mathematical Methods in Optimization of Differential Systems

Partial Differential Equations and Boundary Value Problems

Stabilization of Navier–Stokes Flows

Stabilization of Navier-Stokes Flows

Analysis and Optimization of Differential Systems

Nonlinear Differential Equations of Monotone Types in Banach Spaces

Nonlinear Differential Equations of Monotone Types in Banach Spaces

Stabilization of Navier–Stokes Flows

Nonlinear Differential Equations of Monotone Types in Banach Spaces

Analysis and Optimization of Differential Systems : IFIP TC7 / WG7.2 International Working Conference on Analysis and Optimization of Differential Sys

Analysis and Optimization of Differential Systems

Controllability and Stabilization of Parabolic Equations

Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts

Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts

Stochastic Porous Media Equations

Stochastic Porous Media Equations

Differential Equations

Differential Equations

Controllability and Stabilization of Parabolic Equations

Controllability and Stabilization of Parabolic Equations

Nonlinear semigroups and differential equations in Banach spaces

Partial Differential Equations and Boundary Value Problems

Convexity and Optimization in Banach Spaces

Convexity and Optimization in Banach Spaces

Mathematical Methods in Optimization of Differential Systems

Mathematical Methods in Optimization of Differential Systems

Partial Differential Equations and Boundary Value Problems

Convexity and Optimization in Banach Spaces

SEMIGROUP APPROACH TO NONLINEAR DIFFUSION EQUATIONS