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Blow Up In Nonlinear Equations

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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 In Nonlinear Equations

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Author : Maxim Olegovich Korpusov
language : en
Publisher: Walter de Gruyter
Release Date : 2014-10-15

Blow Up In Nonlinear Equations written by Maxim Olegovich Korpusov 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 2014-10-15 with Science categories.

This book is about the phenomenon ofthe emergence of blow-up effectsin nonlinear equations.In particular it deals with theirapplicationsin modern mathematical physics.The bookmay also serve as a manual for researchers who want toget an overview ofthe main methods in nonlinear analysis.

Blowup For Nonlinear Hyperbolic Equations

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Author : Serge Alinhac
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Blowup For Nonlinear Hyperbolic Equations written by Serge Alinhac 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 2013-12-01 with Mathematics categories.

Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as blowup. In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it.

Blow Up In Nonlinear Sobolev Type Equations

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Author : Alexander B. Al'shin
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-26

Blow Up In Nonlinear Sobolev Type Equations written by Alexander B. Al'shin 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 2011-05-26 with Mathematics categories.

The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.

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.

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

Nonlinear Wave Equations

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Author : Walter A. Strauss
language : en
Publisher: American Mathematical Soc.
Release Date : 1990-01-12

Nonlinear Wave Equations written by Walter A. Strauss 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 1990-01-12 with Mathematics categories.

The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Nonlinear Dynamics And Renormalization Group

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Author : Israel Michael Sigal
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Nonlinear Dynamics And Renormalization Group written by Israel Michael Sigal 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 2001 with Differential equations, Nonlinear categories.

This book contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathématiques (CRM) in Montréal (Canada), as part of the year-long program devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential equations and renormalization group contribute recent results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers the latest research in the rapidly developing fields of nonlinear equations and renormalization group.

Blow Up In Nonlinear Equations

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