Maxim Olegovich Korpusov's Books

Blow-up in Nonlinear Sobolev Type Equations

By: Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov

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Blow-up in Nonlinear Sobolev Type Equations

By: Alexander B. Al'shin,Maxim O. Korpusov,Alexey G. Sveshnikov

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.

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661

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110255294

ISBN 13

9783110255294

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

By: Maxim Olegovich Korpusov,Alexey V Ovchinnikov,Alexander Anatolyevich Panin

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Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

By: Maxim Olegovich Korpusov,Alexey V Ovchinnikov,Alexander Anatolyevich Panin

This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.

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377

Publisher

World Scientific

Published Date

ISBN 10

981124894X

ISBN 13

9789811248948

Blow-Up in Nonlinear Equations of Mathematical Physics

Theory and Methods

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov,Alexey Georgievich Sveshnikov,Egor Vladislavovich Yushkov

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Blow-Up in Nonlinear Equations of Mathematical Physics

Theory and Methods

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov,Alexey Georgievich Sveshnikov,Egor Vladislavovich Yushkov

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

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348

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110602075

ISBN 13

9783110602074

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

By: Maxim Olegovich Korpusov,Alexey V Ovchinnikov,Alexander Anatolyevich Panin

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Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

By: Maxim Olegovich Korpusov,Alexey V Ovchinnikov,Alexander Anatolyevich Panin

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Page Count

377

Publisher

World Scientific

Published Date

ISBN 10

981124894X

ISBN 13

9789811248948

Blow-Up in Nonlinear Equations of Mathematical Physics

Theory and Methods

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov,Alexey Georgievich Sveshnikov,Egor Vladislavovich Yushkov

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Blow-Up in Nonlinear Equations of Mathematical Physics

Theory and Methods

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov,Alexey Georgievich Sveshnikov,Egor Vladislavovich Yushkov

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Page Count

348

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110602075

ISBN 13

9783110602074

Blow-Up in Nonlinear Equations

In Mathematical Physics

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov

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Blow-Up in Nonlinear Equations

In Mathematical Physics

By: Maxim Olegovich Korpusov,Alexey Vital'evich Ovchinnikov

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.

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Page Count

500

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110313049

ISBN 13

9783110313048

Book's by Maxim Olegovich Korpusov

Blow-up in Nonlinear Sobolev Type Equations

Blow-up in Nonlinear Sobolev Type Equations

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Blow-Up in Nonlinear Equations of Mathematical Physics

Blow-Up in Nonlinear Equations of Mathematical Physics

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Blow-Up in Nonlinear Equations of Mathematical Physics

Blow-Up in Nonlinear Equations of Mathematical Physics

Blow-Up in Nonlinear Equations

Blow-Up in Nonlinear Equations

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