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Blow-Up in Nonlinear Equations of Mathematical Physics

2018-08-06 Mathematics
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Release : 2018-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 007/5 ( reviews)

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Book Synopsis Blow-Up in Nonlinear Equations of Mathematical Physics by : Maxim Olegovich Korpusov

Download or read book Blow-Up in Nonlinear Equations of Mathematical Physics written by Maxim Olegovich Korpusov. This book was released on 2018-08-06. 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

Blow-up of solutions of model nonlinear equations of mathematical physics

2013
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Release : 2013
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Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Blow-up of solutions of model nonlinear equations of mathematical physics by : M. O. Korpusov

Download or read book Blow-up of solutions of model nonlinear equations of mathematical physics written by M. O. Korpusov. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt:

Blow-up in Nonlinear Sobolev Type Equations

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 278/5 ( reviews)

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Book Synopsis Blow-up in Nonlinear Sobolev Type Equations by : A. B. Alʹshin

Download or read book Blow-up in Nonlinear Sobolev Type Equations written by A. B. Alʹshin. This book was released on 2011. 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.

Blow-Up in Nonlinear Equations

2014-10-15 Science
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Release : 2014-10-15
Genre : Science
Kind : eBook
Book Rating : 048/5 ( reviews)

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Book Synopsis Blow-Up in Nonlinear Equations by : Maxim Olegovich Korpusov

Download or read book Blow-Up in Nonlinear Equations written by Maxim Olegovich Korpusov. This book was released on 2014-10-15. 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.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics

2006-11-02 Mathematics
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Release : 2006-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 631/5 ( reviews)

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Book Synopsis Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by : Victor A. Galaktionov

Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov. This book was released on 2006-11-02. 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 focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.

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