Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems
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Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems
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Author : Gershon Kresin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-08-15
Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems written by Gershon Kresin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Mathematics categories.
The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems
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Author : Gershon Kresin
language : en
Publisher: American Mathematical Soc.
Release Date :
Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems written by Gershon Kresin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Strongly Coupled Parabolic And Elliptic Systems
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Author : Dung Le
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
Strongly Coupled Parabolic And Elliptic Systems written by Dung Le and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity
Superlinear Parabolic Problems
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Author : Prof. Dr. Pavol Quittner
language : en
Publisher: Springer
Release Date : 2019-06-13
Superlinear Parabolic Problems written by Prof. Dr. Pavol Quittner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.
This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
Complex Analysis And Dynamical Systems Vi
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Author : Matania Ben-Artzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-03
Complex Analysis And Dynamical Systems Vi written by Matania Ben-Artzi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-03 with Mathematics categories.
This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19-24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers in this volume range over a wide variety of topics in Partial Differential Equations, Differential Geometry, and the Radon Transform. Taken together, the articles collected here provide the reader with a panorama of activity in partial differential equations and general relativity, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 667) is devoted to complex analysis, quasiconformal mappings, and complex dynamics. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
The Maz Ya Anniversary Collection
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Author : Jürgen Rossmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Maz Ya Anniversary Collection written by Jürgen Rossmann 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 contributions in this volume are dedicated to Vladimir G. Maz'ya and are par tially based on talks given at the conference "Functional Analysis, Partial Differ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.
Elliptic And Parabolic Equations
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Author : Zhuoqun Wu
language : en
Publisher: World Scientific Publishing Company
Release Date : 2006-10-17
Elliptic And Parabolic Equations written by Zhuoqun Wu and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-17 with Mathematics categories.
This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Elliptic And Parabolic Equations Involving The Hardy Leray Potential
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Author : Ireneo Peral Alonso
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-22
Elliptic And Parabolic Equations Involving The Hardy Leray Potential written by Ireneo Peral Alonso and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Fokker Planck Kolmogorov Equations
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-10
Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups
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Author : Stefano Biagi
language : en
Publisher: World Scientific
Release Date : 2018-12-05
An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups written by Stefano Biagi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-05 with Mathematics categories.
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings: