Singular Solutions of Nonlinear Elliptic and Parabolic Equations, Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov

Автор: Pao, C. V.
Название: Nonlinear parabolic and elliptic equations
ISBN: 1461363233 ISBN-13(EAN): 9781461363231
Издательство: Springer
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Цена: 158380.00 T
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Описание: 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.

Автор: VIOREL BARBU
Название: Controllability and Stabilization of Parabolic Equations
ISBN: 3319766651 ISBN-13(EAN): 9783319766652
Издательство: Springer
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Цена: 93160.00 T
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Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.

Автор: T Jangveladze
Название: Numerical Solutions of Three Classes of Nonlinear Parabolic Integ
ISBN: 0128046287 ISBN-13(EAN): 9780128046289
Издательство: Elsevier Science
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Цена: 116780.00 T
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Описание: This book describes three classes of nonlinear partial integro-differential equations. These models arise in electromagnetic diffusion processes and heat flow in materials with memory. Mathematical modeling of these processes is briefly described in the first chapter of the book. Investigations of the described equations include theoretical as well as approximation properties. Qualitative and quantitative properties of solutions of initial-boundary value problems are performed therafter. All statements are given with easy understandable proofs. For approximate solution of problems different varieties of numerical methods are investigated. Comparison analyses of those methods are carried out. For theoretical results the corresponding graphical illustrations are included in the book. At the end of each chapter topical bibliographies are provided.

Автор: Emmanuele DiBenedetto; Prof. Ugo Pietro Gianazza U
Название: Harnack`s Inequality for Degenerate and Singular Parabolic Equations
ISBN: 1489999760 ISBN-13(EAN): 9781489999764
Издательство: Springer
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Цена: 111790.00 T
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Описание:

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete.

It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p>2 or m>1) and in the singular range (1pmThe book is self-contained. Building on a similar monograph by the first author, the authors of the present book focus entirely on the Harnack estimates and on their applications: indeed a number of known regularity results are given a new proof, based on the Harnack inequality. It is addressed to all professionals active in the field, and also to advanced graduate students, interested in understanding the main issues of this fascinating research field.

Автор: Joachim Escher; Elmar Schrohe; J?rg Seiler; Christ
Название: Elliptic and Parabolic Equations
ISBN: 3319381504 ISBN-13(EAN): 9783319381503
Издательство: Springer
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Цена: 102480.00 T
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Описание: The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations.

Автор: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov
Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations
ISBN: 3110315483 ISBN-13(EAN): 9783110315486
Издательство: Walter de Gruyter
Цена: 223090.00 T
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Описание: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography

Автор: N.V. Krylov
Название: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
ISBN: 1470447401 ISBN-13(EAN): 9781470447403
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Автор: Gershon Kresin, Vladimir Maz`ya
Название: Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems
ISBN: 0821889818 ISBN-13(EAN): 9780821889817
Издательство: Mare Nostrum (Eurospan)
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Цена: 96090.00 T
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Описание: 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.