Blow Up In Nonlinear Equations Of Mathematical Physics
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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.
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.
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.
Partial Differential Equations And Mathematical Physics
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Partial Differential Equations And Mathematical Physics written by Lars Hörmander 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 2013-04-17 with Mathematics categories.
On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support
Blowup For Nonlinear Hyperbolic Equations
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Author : Serge Alinhac
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-04-07
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 1995-04-07 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.
Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations
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Author : Sergey I Piskarev
language : en
Publisher: World Scientific
Release Date : 2023-07-05
Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations written by Sergey I Piskarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-05 with Mathematics categories.
The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
Superlinear Parabolic Problems
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Author : Pavol Quittner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-16
Superlinear Parabolic Problems written by Pavol Quittner 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 2007-12-16 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 book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.
Mathematical Physics And Its Interactions
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Author : Shuji Machihara
language : en
Publisher: Springer Nature
Release Date : 2024-07-03
Mathematical Physics And Its Interactions written by Shuji Machihara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-03 with Mathematics categories.
This publication comprises research papers contributed by the speakers, primarily based on their planned talks at the meeting titled 'Mathematical Physics and Its Interactions,' initially scheduled for the summer of 2021 in Tokyo, Japan. It celebrates Tohru Ozawa's 60th birthday and his extensive contributions in many fields. The works gathered in this volume explore interactions between mathematical physics, various types of partial differential equations (PDEs), harmonic analysis, and applied mathematics. They are authored by research leaders in these fields, and this selection honors the spirit of the workshop by showcasing cutting-edge results and providing a forward-looking perspective through discussions of problems, with the goal of shaping future research directions. Originally planned as an in-person gathering, this conference had to change its format due to limitations imposed by COVID, more precisely to avoid inducing people into unnecessary vaccinations.
Xviith International Congress On Mathematical Physics
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Author : Arne Jensen
language : en
Publisher: World Scientific
Release Date : 2014
Xviith International Congress On Mathematical Physics written by Arne Jensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.
This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.