Victor A. Galaktionov's Books

A Stability Technique for Evolution Partial Differential Equations

A Dynamical Systems Approach

By: Victor A. Galaktionov,Juan Luis Vázquez

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A Stability Technique for Evolution Partial Differential Equations

A Dynamical Systems Approach

By: Victor A. Galaktionov,Juan Luis Vázquez

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

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Page Count

388

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461220505

ISBN 13

9781461220503

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

By: Victor A. Galaktionov,Sergey R. Svirshchevskii

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

By: Victor A. Galaktionov,Sergey R. Svirshchevskii

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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Page Count

538

Publisher

CRC Press

Published Date

ISBN 10

1584886633

ISBN 13

9781584886631

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

By: Victor A. Galaktionov,Enzo L. Mitidieri,Stanislav I. Pohozaev

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Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

By: Victor A. Galaktionov,Enzo L. Mitidieri,Stanislav I. Pohozaev

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book

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565

Publisher

CRC Press

Published Date

ISBN 10

1482251736

ISBN 13

9781482251739

The Struggle for Utopia

Rodchenko, Lissitzky, Moholy-Nagy, 1917-1946

By: Victor Margolin

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The Struggle for Utopia

Rodchenko, Lissitzky, Moholy-Nagy, 1917-1946

By: Victor Margolin

. Focusing on the difficult relationship between art and social change, Margolin brings important new insights to our understanding of the avant-garde's role in a period of great political complexity.

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286

Publisher

University of Chicago Press

Published Date

ISBN 10

0226505162

ISBN 13

9780226505169

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

By: Victor A. Galaktionov

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Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

By: Victor A. Galaktionov

Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un

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Page Count

384

Publisher

CRC Press

Published Date

ISBN 10

0203998065

ISBN 13

9780203998069

Blow-Up in Quasilinear Parabolic Equations

By: A. A. Samarskii,Victor a. Galaktionov,Sergey p. Kurdyumov,A. P. Mikhailov

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Blow-Up in Quasilinear Parabolic Equations

By: A. A. Samarskii,Victor a. Galaktionov,Sergey p. Kurdyumov,A. P. Mikhailov

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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Page Count

561

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110889862

ISBN 13

9783110889864

Book's by Victor A. Galaktionov

A Stability Technique for Evolution Partial Differential Equations

A Stability Technique for Evolution Partial Differential Equations

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

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

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

The Struggle for Utopia

The Struggle for Utopia

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications

Blow-Up in Quasilinear Parabolic Equations

Blow-Up in Quasilinear Parabolic Equations

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