Parabolic Boundary Value Problems
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Parabolic Boundary Value Problems
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Author : Samuil D. Eidelman
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-01
Parabolic Boundary Value Problems written by Samuil D. Eidelman 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 1999-12-01 with Mathematics categories.
The present monograph is devoted to the theory of general parabolic boundary value problems. The vastness of this theory forced us to take difficult decisions in selecting the results to be presented and in determining the degree of detail needed to describe their proofs. In the first chapter we define the basic notions at the origin of the theory of parabolic boundary value problems and give various examples of illustrative and descriptive character. The main part of the monograph (Chapters II to V) is devoted to a the detailed and systematic exposition of the L -theory of parabolic 2 boundary value problems with smooth coefficients in Hilbert spaces of smooth functions and distributions of arbitrary finite order and with some natural appli cations of the theory. Wishing to make the monograph more informative, we included in Chapter VI a survey of results in the theory of the Cauchy problem and boundary value problems in the traditional spaces of smooth functions. We give no proofs; rather, we attempt to compare different results and techniques. Special attention is paid to a detailed analysis of examples illustrating and complementing the results for mulated. The chapter is written in such a way that the reader interested only in the results of the classical theory of the Cauchy problem and boundary value problems may concentrate on it alone, skipping the previous chapters.
Periodic Parabolic Boundary Value Problems And Positivity
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Author : Peter Hess
language : en
Publisher: Longman
Release Date : 1991
Periodic Parabolic Boundary Value Problems And Positivity written by Peter Hess and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
In these notes we give a unified treatment of semilinear nonautonomous diffusion equations and systems thereof, which satisfy a comparison principle, and whose coefficient functions depend periodically on time. Such equations arise naturally, e. g. in biomathematics if one admits dependence of the data on daily, monthly, or seasonal variations. Typical examples considered are the logistic equation with diffusion, Fisher's equation of population genetics, and Volterra-Lotka systems (with diffusion) of competition and of the predator-prey type. The existence and qualitative properties of periodic solutions, and the asymptotic behaviour of solutions of the initial-value problem are studied. Basic underlying concepts are strongly order-preserving discrete semigroups and the principal eigenvalue of a periodic-parabolic operator.
Nonlinear Parabolic And Elliptic Equations
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Author : C.V. Pao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Parabolic And Elliptic Equations written by C.V. Pao 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 2012-12-06 with Mathematics categories.
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Parabolic Boundary Value Problems
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Author : Samuil D. Eidelman
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Parabolic Boundary Value Problems written by Samuil D. Eidelman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present monograph is devoted to the theory of general parabolic boundary value problems. The vastness of this theory forced us to take difficult decisions in selecting the results to be presented and in determining the degree of detail needed to describe their proofs. In the first chapter we define the basic notions at the origin of the theory of parabolic boundary value problems and give various examples of illustrative and descriptive character. The main part of the monograph (Chapters II to V) is devoted to a the detailed and systematic exposition of the L -theory of parabolic 2 boundary value problems with smooth coefficients in Hilbert spaces of smooth functions and distributions of arbitrary finite order and with some natural appli cations of the theory. Wishing to make the monograph more informative, we included in Chapter VI a survey of results in the theory of the Cauchy problem and boundary value problems in the traditional spaces of smooth functions. We give no proofs; rather, we attempt to compare different results and techniques. Special attention is paid to a detailed analysis of examples illustrating and complementing the results for mulated. The chapter is written in such a way that the reader interested only in the results of the classical theory of the Cauchy problem and boundary value problems may concentrate on it alone, skipping the previous chapters.
Well Posedness Of Parabolic Difference Equations
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Author : A. Ashyralyev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Well Posedness Of Parabolic Difference Equations written by A. Ashyralyev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.
Initial Boundary Value Problems And The Navier Stokes Equation
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Author : Heinz-Otto Kreiss
language : en
Publisher: SIAM
Release Date : 2004-01-01
Initial Boundary Value Problems And The Navier Stokes Equation written by Heinz-Otto Kreiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.
Numerical Methods For Elliptic And Parabolic Partial Differential Equations
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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26
Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner 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 2003-06-26 with Mathematics categories.
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Elliptic And Parabolic Equations With Discontinuous Coefficients
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Author : Antonino Maugeri
language : en
Publisher: Wiley-VCH
Release Date : 2000-12-13
Elliptic And Parabolic Equations With Discontinuous Coefficients written by Antonino Maugeri and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-13 with Mathematics categories.
This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.
Second Order Parabolic Differential Equations
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Author : Gary M. Lieberman
language : en
Publisher: World Scientific
Release Date : 1996
Second Order Parabolic Differential Equations written by Gary M. Lieberman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Singular Parabolic Boundary Value Problems
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Author : Benedict Man Lam Wong
language : en
Publisher:
Release Date : 1990
Singular Parabolic Boundary Value Problems written by Benedict Man Lam Wong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Boundary value problems categories.