Marcus Waurick – författare
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12 produkter
12 produkter
Häftad, Engelska, 2020
603 kr
Skickas inom 10-15 vardagar
This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach.The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.
E-bok
Engelska, 2020764 kr
Läs direkt efter köp
This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach.
The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.
Del 287 - Operator Theory: Advances and Applications
Evolutionary Equations
Picard's Theorem for Partial Differential Equations, and Applications
Inbunden, Engelska, 2022
548 kr
Skickas inom 10-15 vardagar
This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed.The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.
Del 287 - Operator Theory: Advances and Applications
Evolutionary Equations
Picard's Theorem for Partial Differential Equations, and Applications
Häftad, Engelska, 2022
440 kr
Skickas inom 10-15 vardagar
This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed.The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.
Inbunden, Engelska, 2024
2 173 kr
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This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:Differential algebraic equationsPort-Hamiltonian systems in both finite and infinite dimensionsHighly nonlinear equations related to elasticity/plasticityModeling of thermo-piezo-electromagnetism
E-bok
Engelska, 20242 741 kr
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This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:
Differential algebraic equationsPort-Hamiltonian systems in both finite and infinite dimensionsHighly nonlinear equations related to elasticity/plasticityModeling of thermo-piezo-electromagnetism
Häftad, Engelska, 2025
2 173 kr
Skickas inom 10-15 vardagar
This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:Differential algebraic equationsPort-Hamiltonian systems in both finite and infinite dimensionsHighly nonlinear equations related to elasticity/plasticityModeling of thermo-piezo-electromagnetism
E-bok
Engelska, 2025611 kr
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This book investigates homogenisation problems for divergence form equations with rapidly sign-changing coefficients. Focusing on problems with piecewise constant, scalar coefficients in a (d-dimensional) crosswalk type shape, we will provide a limit procedure in order to understand potentially ill-posed and non-coercive settings.Depending on the integral mean of the coefficient and its inverse, the limits can either satisfy the usual homogenisation formula for stratified media, be entirely degenerate or be a non-local differential operator of 4th order. In order to mark the drastic change of nature, we introduce the ‘inner spectrum’ for conductivities. We show that even though 0 is contained in the inner spectrum for all strictly positive periods, the limit inner spectrum can be empty. Furthermore, even though the spectrum was confined in a bounded set uniformly for all strictly positive periods and not containing 0, the limit inner spectrum might have 0 as an essential spectral point and accumulate at ∞ or even be the whole of C. This is in stark contrast to the classical situation, where it is possible to derive upper and lower bounds in terms of the values assumed by the coefficients in the pre-asymptotics.Along the way, we also develop a theory for Sturm–Liouville type operators with indefinite weights, reduce the question on solvability of the associated Sturm–Liouville operator to understanding zeros of a certain explicit polynomial and show that generic real perturbations of piecewise constant coefficients lead to continuously invertible Sturm–Liouville expressions.
Häftad, Engelska, 2025
494 kr
Skickas inom 10-15 vardagar
This book investigates homogenisation problems for divergence form equations with rapidly sign-changing coefficients. Focusing on problems with piecewise constant, scalar coefficients in a (d-dimensional) crosswalk type shape, we will provide a limit procedure in order to understand potentially ill-posed and non-coercive settings.Depending on the integral mean of the coefficient and its inverse, the limits can either satisfy the usual homogenisation formula for stratified media, be entirely degenerate or be a non-local differential operator of 4th order. In order to mark the drastic change of nature, we introduce the ‘inner spectrum’ for conductivities. We show that even though 0 is contained in the inner spectrum for all strictly positive periods, the limit inner spectrum can be empty. Furthermore, even though the spectrum was confined in a bounded set uniformly for all strictly positive periods and not containing 0, the limit inner spectrum might have 0 as an essential spectral point and accumulate at ∞ or even be the whole of C. This is in stark contrast to the classical situation, where it is possible to derive upper and lower bounds in terms of the values assumed by the coefficients in the pre-asymptotics.Along the way, we also develop a theory for Sturm–Liouville type operators with indefinite weights, reduce the question on solvability of the associated Sturm–Liouville operator to understanding zeros of a certain explicit polynomial and show that generic real perturbations of piecewise constant coefficients lead to continuously invertible Sturm–Liouville expressions.
Inbunden, Engelska, 2026
1 669 kr
Kommande
This book covers work in the broad area of the scientific interests of Rainer Picard’s research work marking Rainer’s 80th birthday. Thus, it contains numerous articles provided by his friends and colleagues from the areas of partial differential equations — both time-dependent and time-independent — from operator theory including topics such as monotonicity and particular operator theoretic applications to questions arising in partial differential equations or numerics, and from mathematical physics detailing the impact of functional analysis to the most recent models describing physical processes in nature.
Del 2157 - Lecture Notes in Mathematics
Callias Index Formula Revisited
Häftad, Engelska, 2016
386 kr
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These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
E-bok
PDF, Engelska, 2016428 kr
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These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.