A Basic Guide To Uniqueness Problems For Evolutionary Differential Equations
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A Basic Guide To Uniqueness Problems For Evolutionary Differential Equations
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Author : Mi-Ho Giga
language : en
Publisher: Springer Nature
Release Date : 2023-09-14
A Basic Guide To Uniqueness Problems For Evolutionary Differential Equations written by Mi-Ho Giga and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.
This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2011-09-22
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.
The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionarypartial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell'scapability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class ofnon-linear equations is investigated, with applications to stochastic control and differential games.The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.- Volume 1 focuses on the abstract theory of evolution- Volume 2 considers more concrete probelms relating to specific applications- Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs
Phase Transitions And Hysteresis
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Author : Augusto Visintin
language : en
Publisher: Springer
Release Date : 2006-11-15
Phase Transitions And Hysteresis written by Augusto Visintin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques. 2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Müller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate. 3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2001
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Motion By Mean Curvature And Related Topics
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Author : Giuseppe Buttazzo
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Motion By Mean Curvature And Related Topics written by Giuseppe Buttazzo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1992
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Aeronautics categories.
Energy Optimization In Process Systems
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Author : Stanislaw Sieniutycz
language : en
Publisher: Elsevier
Release Date : 2009-05-06
Energy Optimization In Process Systems written by Stanislaw Sieniutycz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-06 with Technology & Engineering categories.
Despite the vast research on energy optimization and process integration, there has to date been no synthesis linking these together. This book fills the gap, presenting optimization and integration in energy and process engineering. The content is based on the current literature and includes novel approaches developed by the authors. Various thermal and chemical systems (heat and mass exchangers, thermal and water networks, energy converters, recovery units, solar collectors, and separators) are considered. Thermodynamics, kinetics and economics are used to formulate and solve problems with constraints on process rates, equipment size, environmental parameters, and costs. Comprehensive coverage of dynamic optimization of energy conversion systems and separation units is provided along with suitable computational algorithms for deterministic and stochastic optimization approaches based on: nonlinear programming, dynamic programming, variational calculus, Hamilton-Jacobi-Bellman theory, Pontryagin's maximum principles, and special methods of process integration. Integration of heat energy and process water within a total site is shown to be a significant factor reducing production costs, in particular costs of utilities for the chemical industry. This integration involves systematic design and optimization of heat exchangers and water networks (HEN and WN). After presenting basic, insight-based Pinch Technology, systematic, optimization-based sequential and simultaneous approaches to design HEN and WN are described. Special consideration is given to the HEN design problem targeting stage, in view of its importance at various levels of system design. Selected, advanced methods for HEN synthesis and retrofit are presented. For WN design a novel approach based on stochastic optimization is described that accounts for both grassroot and revamp design scenarios. - Presents a unique synthesis of energy optimization and process integration that applies scientific information from thermodynamics, kinetics, and systems theory - Discusses engineering applications including power generation, resource upgrading, radiation conversion and chemical transformation, in static and dynamic systems - Clarifies how to identify thermal and chemical constraints and incorporate them into optimization models and solutions
Hyperbolic Conservation Laws In Continuum Physics
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Author : Constantine M. Dafermos
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-12
Hyperbolic Conservation Laws In Continuum Physics written by Constantine M. Dafermos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-12 with Mathematics categories.
The aim of this work is to present a broad overview of the theory of hyperbolic c- servation laws, with emphasis on its genetic relation to classical continuum physics. It was originally published a decade ago, and a second, revised edition appeared in 2005. It is a testament to the vitality of the ?eld that in order to keep up with - cent developments it has become necessary to prepare a substantially expanded and updated new edition. A new chapter has been added, recounting the exciting recent developmentsin classical open problems in compressible ?uid ?ow. Still another - dition is an account of the early history of the subject, which had an interesting, - multuous childhood. Furthermore, a substantial portion of the original text has been reorganized so as to streamline the exposition, update the information, and enrich the collection of examples. In particular, Chapter V has been completely revised. The bibliography has been updated and expanded as well, now comprising over - teenhundred titles. The background, scope, and plan of the book are outlined in the Introduction, following this preface. Geometric measure theory, functional analysis and dynamical systems provide the necessary tools in the theory of hyperbolic conservation laws, but to a great - tent the analysis employscustom-madetechniques,with strong geometric?avor, - derscoring wave propagation and wave interactions. This may leave the impression that the area is insular, detached from the mainland of partial differential equations.
Optimizing Thermal Chemical And Environmental Systems
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Author : Stanislaw Sieniutycz
language : en
Publisher: Elsevier
Release Date : 2017-11-13
Optimizing Thermal Chemical And Environmental Systems written by Stanislaw Sieniutycz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-13 with Science categories.
Optimizing Thermal, Chemical and Environmental Systems treats the evaluation of power or energy limits for processes that arise in various thermal, chemical and environmental engineering systems (heat and mass exchangers, power converters, recovery units, solar collectors, mixture separators, chemical reactors, catalyst regenerators, etc.). The book is an indispensable source for researchers and students, providing the necessary information on what has been achieved to date in the field of process optimization, new research problems, and what kind of further studies should be developed within quite specialized optimizations. - Summarizes recent achievements of advanced optimization techniques - Links exergy definitions in reversible systems with classical problems of extremum work - Includes practical problems and illustrative examples to clarify applications - Provides a unified description of classical and work-assisted heat and mass exchangers - Written by a first-class expert in the field of advanced methods in thermodynamics
American Scientist
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Author :
language : en
Publisher:
Release Date : 1942
American Scientist written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1942 with Greek letter societies categories.