Download or read book Blow Up in Nonlinear Equations of Mathematical Physics written by Maxim Olegovich Korpusov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Blow Up in Nonlinear Equations written by Maxim Olegovich Korpusov and published by Walter de Gruyter. This book was released on 2014-10-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Blow up in Nonlinear Sobolev Type Equations written by Alexander B. Al'shin and published by Walter de Gruyter. This book was released on 2011-05-26 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonlinear and Modern Mathematical Physics written by Solomon Manukure and published by Springer Nature. This book was released on with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Dynamics and Renormalization Group written by Israel Michael Sigal and published by American Mathematical Soc.. This book was released on 2001 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nelinejnye Nelokal nye Uravneni V Teorii Voln written by Pavel Ivanovich Naumkin and published by American Mathematical Soc.. This book was released on with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov and published by CRC Press. This book was released on 2006-11-02 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Nonlinear Wave Equations written by Walter A. Strauss and published by American Mathematical Soc.. This book was released on 1990-01-12 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Blow up Theory for Elliptic PDEs in Riemannian Geometry MN 45 written by Olivier Druet and published by Princeton University Press. This book was released on 2009-01-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Selfdual Gauge Field Vortices written by Gabriella Tarantello and published by Springer Science & Business Media. This book was released on 2008-04-16 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses specific examples of selfdual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern–Simons–Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices.

Download or read book Nonlinear PDE s Dynamics and Continuum Physics written by J. L. Bona and published by American Mathematical Soc.. This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Explosive Instabilities in Mechanics written by Brian Straughan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with explosive instabilities in mechanics, deriving a solution to a system of PDEs that arise in practical situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations. Among the topics presented are: classical fluid equations, catastrophic behavior in nonlinear fluid theories, blow-up in Volterra equations, and rapid energy growth in parallel flows.

Download or read book Microlocal Methods in Mathematical Physics and Global Analysis written by Daniel Grieser and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.​

Download or read book Advances in Differential Equations and Mathematical Physics written by Yulia E. Karpeshina and published by American Mathematical Soc.. This book was released on 2003 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics. Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudodifferential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and nonequilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.

Download or read book Nonlinear Stochastic Systems In Physics And Mechanics written by Bellomo Nicola and published by World Scientific. This book was released on 1987-03-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the conceptional line which goes from the observation of physical systems to their modeling and analysis by ordinary differential nonlinear stochastic equations.First, the problems of the mathematical modeling of physical systems are developed. These mathematical models are then classified in terms of ordinary differential stochastic equations from which both qualitative and quantitative results are developed.Each one of the various subjects are methods dealt with ends with an application in mathematical physics or in nonlinear mechanics.