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29 produkter
29 produkter
E-bok
Engelska, 19971 978 kr
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Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary.The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration.- Provides the first unified survey of the advances made in the last 15 years in the field- Includes an up-to-date compendium of the mathematical literature on these topics
Inbunden, Engelska, 2003
1 080 kr
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This book is a revised edition of my earlier book of the same title. The cur rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.
E-bok
PDF, Engelska, 20131 416 kr
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This book is a revised edition of my earlier book of the same title. The cur rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.
Inbunden, Engelska, 2008
1 080 kr
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This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.
E-bok
PDF, Engelska, 20081 367 kr
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This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.
E-bok
PDF, Engelska, 20151 006 kr
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This book focuses on the modelling of contemporary health and social problems, especially those considered a major burden to communities, governments and taxpayers, such as smoking, alcoholism, drug use, and heart disease. Based on a series of papers presented at a recent conference hosted by the Leverhulme-funded Tipping Points project at the University of Durham, this book illustrates a broad range of modelling approaches. Such a diverse collection demonstrates that an interdisciplinary approach is essential to modelling tipping points in health and social problems, and the assessment of associated risk and resilience.
E-bok
Engelska, 20151 006 kr
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This book focuses on the modelling of contemporary health and social problems, especially those considered a major burden to communities, governments and taxpayers, such as smoking, alcoholism, drug use, and heart disease. Based on a series of papers presented at a recent conference hosted by the Leverhulme-funded Tipping Points project at the University of Durham, this book illustrates a broad range of modelling approaches. Such a diverse collection demonstrates that an interdisciplinary approach is essential to modelling tipping points in health and social problems, and the assessment of associated risk and resilience.
Del 91 - Applied Mathematical Sciences
Energy Method, Stability, and Nonlinear Convection
Häftad, Engelska, 2010
1 080 kr
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This book is a revised edition of my earlier book of the same title. The cur rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.
Del 165 - Applied Mathematical Sciences
Stability and Wave Motion in Porous Media
Häftad, Engelska, 2010
1 080 kr
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This book presents an account of theories of ?ow in porous media which have proved tractable to analysis and computation. In particular, the t- ories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, we study the theory of voids in an elastic material due to J. Nunziato and S. Cowin. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under cons- eration, and spatial stability are investigated. We believe this is the ?rst such account of these topics in book form. Throughout, we include several new results not published elsewhere. Temporal stability studies of a variety of problems are included, indic- ingpracticalapplicationsofeach.Bothlinearinstabilityanalysisandglobal nonlinear stability thresholds are presented where possible. The mundane, importantproblemofstabilityof?owinasituationwhereaporousmedium adjoins a clear ?uid is also investigated in some detail. In particular, the chapter dealing with this problem contains some new material only p- lished here. Since stability properties inevitably end up requiring to solve a multi-parameter eigenvalue problem by computational means, a separate chapter is devoted to this topic. Contemporary methods for solving such eigenvalue problems are presented in some detail.
Inbunden, Engelska, 2011
1 669 kr
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This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.
E-bok
PDF, Engelska, 20112 077 kr
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This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest.
This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.
Del 177 - Applied Mathematical Sciences
Heat Waves
Häftad, Engelska, 2013
1 669 kr
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This book surveys significant modern contributions to the mathematical theories of generalized heat wave equations. The first three chapters form a comprehensive survey of most modern contributions also describing in detail the mathematical properties of each model. Acceleration waves and shock waves are the focus in the next two chapters. Numerical techniques, continuous data dependence, and spatial stability of the solution in a cylinder, feature prominently among other topics treated in the following two chapters. The final two chapters are devoted to a description of selected applications and the corresponding formation of mathematical models. Illustrations are taken from a broad range that includes nanofluids, porous media, thin films, nuclear reactors, traffic flow, biology, and medicine, all of contemporary active technological importance and interest. This book will be of value to applied mathematicians, theoretical engineers and other practitioners who wish to know both the theory and its relevance to diverse applications.
E-bok
PDF, Engelska, 20131 100 kr
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The writing of this book was begun during the academic year 1984-1985 while I was a visiting Associate Professor at the University of Wyoming. I am extremely grateful to the people there for their help, in particular to Dick Ewing, Jack George and Robert Gunn, and to Ken Gross, who is now at the University of Vermont. A major part of the first draft of this book was written while I was a visiting Professor at the University of South Carolina during the academic year 1988-1989. I am indebted to the people there for their help, in one way or another, particularly to Ron DeVore, Steve Dilworth, Bob Sharpley, Dave Walker, and especially to the chairman of the Mathematics Department at the University of South Carolina, Colin Bennett. I also wish to express my sincere gratitude to Ray Ogden and Profes sor I.N. Sneddon, F.R.S., both of Glasgow University, for their help over a number of years. I also wish to record my thanks to Ron Hills and Paul Roberts, F.R.S., for giving me a copy of their paper on the Boussinesq ap proximation prior to publication and for allowing me to describe their work here. I should like to thank my Ph.D. student Geoff McKay for spotting several errors and misprints in an early draft. Finally, I am very grateful to an anonymous reviewer for several pertinent suggestions regarding the energy-Casimir method.
Inbunden, Engelska, 2024
1 509 kr
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This monograph provides an account of thermal convection with a focus on Cattaneo’s heat flux equation. Various applications of the equation are analyzed, such as those pertaining to nanoscale mechanics, nuclear engineering, the treatment of various diseases, and more. The influence it has had on problems in the field of thermal convection is highlighted as well. Several other important topics are incorporated, including:Guyer-Krumhansl termsKelvin-Voigt fluid theoryNavier-Stokes theoryHigher gradient fluid theoriesThermal Convection with a Cattaneo Flux Law will appeal to researchers interested in exploring this active area.
E-bok
PDF, Engelska, 20241 832 kr
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This monograph provides an account of thermal convection with a focus on Cattaneo’s heat flux equation. Various applications of the equation are analyzed, such as those pertaining to nanoscale mechanics, nuclear engineering, the treatment of various diseases, and more. The influence it has had on problems in the field of thermal convection is highlighted as well. Several other important topics are incorporated, including:
Guyer-Krumhansl termsKelvin-Voigt fluid theoryNavier-Stokes theoryHigher gradient fluid theoriesThermal Convection with a Cattaneo Flux Law will appeal to researchers interested in exploring this active area.
Häftad, Engelska, 2025
1 509 kr
Skickas inom 10-15 vardagar
This monograph provides an account of thermal convection with a focus on Cattaneo’s heat flux equation. Various applications of the equation are analyzed, such as those pertaining to nanoscale mechanics, nuclear engineering, the treatment of various diseases, and more. The influence it has had on problems in the field of thermal convection is highlighted as well. Several other important topics are incorporated, including:Guyer-Krumhansl termsKelvin-Voigt fluid theoryNavier-Stokes theoryHigher gradient fluid theoriesThermal Convection with a Cattaneo Flux Law will appeal to researchers interested in exploring this active area.
Inbunden, Engelska, 2026
1 616 kr
Skickas inom 5-8 vardagar
This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations. The author's analysis of these equations concentrates on thermal convection in a layer of incompressible fluid. Readers will learn how the Navier-Stokes equations, the Kelvin-Voigt equations, and the Navier-Stokes-Voigt equations are special cases of the generalized Oskolkov system. Thermal convection and double-diffusive convection are studied in Navier-Stokes-Voigt fluids and in various Kelvin-Voigt and Oskolkov fluids. Cutting edge research is included on magnetohydrodynamic convection in a Navier-Stokes-Voigt fluid and in a Kelvin-Voigt fluid of order one.Oskolkov Equations and Thermal Convection will serve as a timely resource for students and researchers interested in this active topic, as well as those studying the broader area of fluid dynamics.
E-bok
PDF, Engelska, 20262 049 kr
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This monograph offers an overview of the active research area involving the class of PDEs known as Oskolkov equations. The author's analysis of these equations concentrates on thermal convection in a layer of incompressible fluid. Readers will learn how the Navier-Stokes equations, the Kelvin-Voigt equations, and the Navier-Stokes-Voigt equations are special cases of the generalized Oskolkov system. Thermal convection and double-diffusive convection are studied in Navier-Stokes-Voigt fluids and in various Kelvin-Voigt and Oskolkov fluids. Cutting edge research is included on magnetohydrodynamic convection in a Navier-Stokes-Voigt fluid and in a Kelvin-Voigt fluid of order one.Oskolkov Equations and Thermal Convection will serve as a timely resource for students and researchers interested in this active topic, as well as those studying the broader area of fluid dynamics.
Inbunden, Engelska, 2015
1 294 kr
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This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.
E-bok
PDF, Engelska, 20151 138 kr
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This book is one of the first devoted to an account of theories of thermal convection which involve local thermal non-equilibrium effects, including a concentration on microfluidic effects. The text introduces convection with local thermal non-equilibrium effects in extraordinary detail, making it easy for readers newer to the subject area to understand. This book is unique in the fact that it addresses a large number of convection theories and provides many new results which are not available elsewhere. This book will be useful to researchers from engineering, fluid mechanics, and applied mathematics, particularly those interested in microfluidics and porous media.
Inbunden, Engelska, 2017
618 kr
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This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.
E-bok
PDF, Engelska, 2017703 kr
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This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.
Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion.This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.
Häftad, Engelska, 2018
618 kr
Skickas inom 10-15 vardagar
This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.
Inbunden, Engelska, 2001
1 080 kr
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This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his PhD, Professor Hutter returned to Europe where he worked as a senior scientist at the Labor atory for Hydraulics, Hydrology and Glaciology, ETH Zurich, being involved in glacier flow, physical limnology, avalanche research and granular media. At the same time he maintained scientific contact with the Mechanics Institute of the Vienna University of Technology. In both European cities he received a habil itation degree: In Vienna for Mechanics, in Zurich for Theoretical Glaciology and Limnology. Since 1987 Professor Hutter has been the successor to Professor Becker at the Department of Mechanics, Darmstadt University of Technology. Professor Hutter's work has always been relevant to reallife, and a feature of the man is his attention to experiments and matching theory. He has built up an internationally respected laboratory in Darmstadt which concentrates on both experimental and theoretical aspects.
Inbunden, Engelska, 1998
543 kr
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The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial differential equation has been an area of intense re search activity in mathematics. Some ofthe early techniques and results were discussed in the monograph by Payne (1975) and in my earlier monograph, Straughan (1982). Relatively recent accounts of blow-up work in partial dif ferential equations may be found in the review by Levine (1990) and in the book by Samarskii et al. (1994). It is becoming increasingly clear that very rapid instabilities and, indeed, finite time blow-up are being witnessed also in problems in applied mathematics and mechanics. Also in vogue in the mathematical literature are studies of blow-up in systems of partial differen tial equations, partial differential equations with non-linear convection terms, and systems of partial differential equations which contain convection terms. Such equations are often derived from models of mundane situations in real life. This book is an account of these topics in a selection of areas of applied mathematics which either I have worked in or I find particularly interesting and deem relevant to be included in such an exposition. I believe the results given in Chap. 2 and Sects. 4. 2. 3 and 4. 2. 4 are new. This research was partly supported by a Max Planck Forschungspreis from the Alexander von Humboldt Foundation and the Max Planck Institute.
Häftad, Engelska, 2010
1 080 kr
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This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his PhD, Professor Hutter returned to Europe where he worked as a senior scientist at the Labor atory for Hydraulics, Hydrology and Glaciology, ETH Zurich, being involved in glacier flow, physical limnology, avalanche research and granular media. At the same time he maintained scientific contact with the Mechanics Institute of the Vienna University of Technology. In both European cities he received a habil itation degree: In Vienna for Mechanics, in Zurich for Theoretical Glaciology and Limnology. Since 1987 Professor Hutter has been the successor to Professor Becker at the Department of Mechanics, Darmstadt University of Technology. Professor Hutter's work has always been relevant to reallife, and a feature of the man is his attention to experiments and matching theory. He has built up an internationally respected laboratory in Darmstadt which concentrates on both experimental and theoretical aspects.
E-bok
PDF, Engelska, 2012712 kr
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The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial differential equation has been an area of intense re search activity in mathematics. Some ofthe early techniques and results were discussed in the monograph by Payne (1975) and in my earlier monograph, Straughan (1982). Relatively recent accounts of blow-up work in partial dif ferential equations may be found in the review by Levine (1990) and in the book by Samarskii et al. (1994). It is becoming increasingly clear that very rapid instabilities and, indeed, finite time blow-up are being witnessed also in problems in applied mathematics and mechanics. Also in vogue in the mathematical literature are studies of blow-up in systems of partial differen tial equations, partial differential equations with non-linear convection terms, and systems of partial differential equations which contain convection terms. Such equations are often derived from models of mundane situations in real life. This book is an account of these topics in a selection of areas of applied mathematics which either I have worked in or I find particularly interesting and deem relevant to be included in such an exposition. I believe the results given in Chap. 2 and Sects. 4. 2. 3 and 4. 2. 4 are new. This research was partly supported by a Max Planck Forschungspreis from the Alexander von Humboldt Foundation and the Max Planck Institute.
Häftad, Engelska, 2012
543 kr
Skickas inom 10-15 vardagar
The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial differential equation has been an area of intense re search activity in mathematics. Some ofthe early techniques and results were discussed in the monograph by Payne (1975) and in my earlier monograph, Straughan (1982). Relatively recent accounts of blow-up work in partial dif ferential equations may be found in the review by Levine (1990) and in the book by Samarskii et al. (1994). It is becoming increasingly clear that very rapid instabilities and, indeed, finite time blow-up are being witnessed also in problems in applied mathematics and mechanics. Also in vogue in the mathematical literature are studies of blow-up in systems of partial differen tial equations, partial differential equations with non-linear convection terms, and systems of partial differential equations which contain convection terms. Such equations are often derived from models of mundane situations in real life. This book is an account of these topics in a selection of areas of applied mathematics which either I have worked in or I find particularly interesting and deem relevant to be included in such an exposition. I believe the results given in Chap. 2 and Sects. 4. 2. 3 and 4. 2. 4 are new. This research was partly supported by a Max Planck Forschungspreis from the Alexander von Humboldt Foundation and the Max Planck Institute.
E-bok
PDF, Engelska, 20131 367 kr
Läs direkt efter köp
This book is dedicated to Professor Kolumban Hutter of the Darmstadt Univer sity of Technology on the occasion of his 60th birthday on 22 January 200l. Professor Hutter graduated in Civil Engineering from the ETH Zurich, and then worked in industry-related consulting at the Institute of Mechanics and the Laboratory of Hydraulics and Soil Mechanics at the ETH, before embark ing on a PhD in Theoretical and Applied Mechanics in Cornell University. He duly completed his PhD under the supervision of Professor Y. H. Pao, working in the field of the electrodynamics of continuous media. After his PhD, Professor Hutter returned to Europe where he worked as a senior scientist at the Labor atory for Hydraulics, Hydrology and Glaciology, ETH Zurich, being involved in glacier flow, physical limnology, avalanche research and granular media. At the same time he maintained scientific contact with the Mechanics Institute of the Vienna University of Technology. In both European cities he received a habil itation degree: In Vienna for Mechanics, in Zurich for Theoretical Glaciology and Limnology. Since 1987 Professor Hutter has been the successor to Professor Becker at the Department of Mechanics, Darmstadt University of Technology. Professor Hutter''s work has always been relevant to reallife, and a feature of the man is his attention to experiments and matching theory. He has built up an internationally respected laboratory in Darmstadt which concentrates on both experimental and theoretical aspects.