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 And Modern Mathematical Physics
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Author : Solomon Manukure
language : en
Publisher: Springer Nature
Release Date :
Nonlinear And Modern Mathematical Physics written by Solomon Manukure and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Nelinejnye Nelokal Nye Uravneni V Teorii Voln
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Author : Pavel Ivanovich Naumkin
language : en
Publisher: American Mathematical Soc.
Release Date :
Nelinejnye Nelokal Nye Uravneni V Teorii Voln written by Pavel Ivanovich Naumkin 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 Science categories.
This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.
Nonlinear Wave Equations
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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 2021-05-30
Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-30 with Mathematics categories.
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics
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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics 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 2006-11-02 with Mathematics categories.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book
Blow Up Theory For Elliptic Pdes In Riemannian Geometry Mn 45
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Author : Olivier Druet
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Blow Up Theory For Elliptic Pdes In Riemannian Geometry Mn 45 written by Olivier Druet and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.
Nonlinear Pde S Dynamics And Continuum Physics
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Author : J. L. Bona
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Nonlinear Pde S Dynamics And Continuum Physics written by J. L. Bona 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 2000 with Mathematics categories.
This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.