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Parabolic Boundary Value Problems
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Book Synopsis Parabolic Boundary Value Problems by : Samuil D. Eidelman
Download or read book Parabolic Boundary Value Problems written by Samuil D. Eidelman and published by Birkhäuser. This book was released on 2012-12-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Periodic-parabolic Boundary Value Problems and Positivity by : Peter Hess
Download or read book Periodic-parabolic Boundary Value Problems and Positivity written by Peter Hess and published by Longman. This book was released on 1991 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents for the first time in book form the results and techniques of such wide ranging studies as Fisher's equation of population genetics and Volterra-Lotkta systems (with diffusion) of competition and of the predator-prey type.
Book Synopsis Nonlinear Parabolic and Elliptic Equations by : C.V. Pao
Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Second Order Parabolic Equations by : Mingxin Wang
Download or read book Nonlinear Second Order Parabolic Equations written by Mingxin Wang and published by CRC Press. This book was released on 2021-05-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parabolic partial differential equations model one of the most important processes in the real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of species in ecology, the diffusion of chemicals in biochemical processes, or the diffusion of information in social networks, diffusion processes are ubiquitous and crucial in the physical and natural world as well as our everyday lives. This book is self-contained and covers key topics such as the Lp theory and Schauder theory, maximum principle, comparison principle, regularity and uniform estimates, initial-boundary value problems of semilinear parabolic scalar equations and weakly coupled parabolic systems, the upper and lower solutions method, monotone properties and long-time behaviours of solutions, convergence of solutions and stability of equilibrium solutions, global solutions and finite time blowup. It also touches on periodic boundary value problems, free boundary problems, and semigroup theory. The book covers major theories and methods of the field, including topics that are useful but hard to find elsewhere. This book is based on tried and tested teaching materials used at the Harbin Institute of Technology over the past ten years. Special care was taken to make the book suitable for classroom teaching as well as for self-study among graduate students. About the Author: Mingxin Wang is Professor of Mathematics at Harbin Institute of Technology, China. He has published ten monographs and textbooks and 260 papers. He is also a supervisor of 30 PhD students.
Book Synopsis Well-Posedness of Parabolic Difference Equations by : A. Ashyralyev
Download or read book Well-Posedness of Parabolic Difference Equations written by A. Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partial Differential Equations of Parabolic Type by : Avner Friedman
Download or read book Partial Differential Equations of Parabolic Type written by Avner Friedman and published by Courier Corporation. This book was released on 2013-08-16 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.
Book Synopsis Initial-boundary Value Problems and the Navier-Stokes Equations by : Heinz-Otto Kreiss
Download or read book Initial-boundary Value Problems and the Navier-Stokes Equations written by Heinz-Otto Kreiss and published by SIAM. This book was released on 1989-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. 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 reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Author :Emmanuele DiBenedetto Publisher :Springer Science & Business Media ISBN 13 :1461208955 Total Pages :402 pages Book Rating :4.4/5 (612 download)
Book Synopsis Degenerate Parabolic Equations by : Emmanuele DiBenedetto
Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Book Synopsis Second Order Parabolic Differential Equations by : Gary M. Lieberman
Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 1996 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Elliptic and Parabolic Equations in Holder Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Holder Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 1996 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
Book Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Initial Boundary Value Problems for Incompletely Parabolic Systems by : J. C. Strikwerda
Download or read book Initial Boundary Value Problems for Incompletely Parabolic Systems written by J. C. Strikwerda and published by . This book was released on 1976 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with initial boundary value problems for incompletely parabolic systems of partial differential equations. Such systems can be described as a second order Petrovskii parabolic system and a first order hyperbolic system coupled together by terms with first order spatial derivatives. The dependent variables are then of either parabolic or hyperbolic type. Examples are the equations for couple sound and heat flow and the viscous shallow water equations.
Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga A. Ladyženskaja
Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1988 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Book Synopsis Non-Homogeneous Boundary Value Problems and Applications by : Jacques Louis Lions
Download or read book Non-Homogeneous Boundary Value Problems and Applications written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Book Synopsis Elliptic and Parabolic Equations with Discontinuous Coefficients by : Antonino Maugeri
Download or read book Elliptic and Parabolic Equations with Discontinuous Coefficients written by Antonino Maugeri and published by Wiley-VCH. This book was released on 2000-12-13 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moving Interfaces and Quasilinear Parabolic Evolution Equations by : Jan Prüss
Download or read book Moving Interfaces and Quasilinear Parabolic Evolution Equations written by Jan Prüss and published by Birkhäuser. This book was released on 2016-07-25 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Book Synopsis Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by : Nikolaĭ Vladimirovich Krylov
Download or read book Lectures on Elliptic and Parabolic Equations in Sobolev Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 2008 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.
