Blow Up In Quasilinear Parabolic Equations

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Blow Up In Quasilinear Parabolic Equations

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Author : A. A. Samarskii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24

Blow Up In Quasilinear Parabolic Equations written by A. A. Samarskii 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 2011-06-24 with Mathematics categories.

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Blow Up For Higher Order Parabolic Hyperbolic Dispersion And Schrodinger Equations

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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2014-09-22

Blow Up For Higher Order Parabolic Hyperbolic Dispersion And Schrodinger Equations written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book

Blow Up Theories For Semilinear Parabolic Equations

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Author : Bei Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-23

Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu 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 2011-03-23 with Mathematics categories.

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Degenerate Parabolic Equations

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Author : Emmanuele DiBenedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Degenerate Parabolic Equations written by Emmanuele DiBenedetto 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.

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.

Singular Solutions Of Nonlinear Elliptic And Parabolic Equations

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Author : Alexander A. Kovalevsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-03-21

Singular Solutions Of Nonlinear Elliptic And Parabolic Equations written by Alexander A. Kovalevsky 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 2016-03-21 with Mathematics categories.

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: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Blow Up In Nonlinear Equations Of Mathematical Physics

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Author : Maxim Olegovich Korpusov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06

Blow Up In Nonlinear Equations Of Mathematical Physics written by Maxim Olegovich Korpusov 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 2018-08-06 with Mathematics categories.

The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results

Blow Up Theories For Semilinear Parabolic Equations

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Author : Bei Hu
language : en
Publisher: Springer
Release Date : 2011-03-17

Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-17 with Mathematics categories.

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Potential Estimates And Quasilinear Parabolic Equations With Measure Data

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Author : Quoc-Hung Nguyen
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-19

Potential Estimates And Quasilinear Parabolic Equations With Measure Data written by Quoc-Hung Nguyen 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 2024-01-19 with Mathematics categories.

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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.

Geometric Sturmian Theory Of Nonlinear Parabolic Equations And Applications

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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2004-05-24

Geometric Sturmian Theory Of Nonlinear Parabolic Equations And Applications written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-24 with Mathematics categories.

Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Pólya in the 1930's and rediscovered in part several times since, it was not until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications. Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications focuses on geometric aspects of the intersection comparison for nonlinear models creating finite-time singularities. After introducing the original Sturm zero set results for linear parabolic equations and the basic concepts of geometric analysis, the author presents the main concepts and regularity results of the geometric intersection theory (G-theory). Here he considers the general singular equation and presents the geometric notions related to the regularity and interface propagation of solutions. In the general setting, the author describes the main aspects of the ODE-PDE duality, proves existence and nonexistence theorems, establishes uniqueness and optimal Bernstein-type estimates, and derives interface equations, including higher-order equations. The final two chapters explore some special aspects of discontinuous and continuous limit semigroups generated by singular parabolic equations. Much of the information presented here has never before been published in book form. Readable and self-contained, this book forms a unique and outstanding reference on second-order parabolic PDEs used as models for a wide range of physical problems.