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

Victor A. Galaktionov

ISBN 10: 0367389975 / ISBN 13: 9780367389970

Verlag: Chapman And Hall/CRC, 2019

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - Providing exact solutions of more than 200 nonlinear equations and models, this book begins with classical as well as more recent examples of interesting solutions on linear invariant subspaces for nonlinear operators. In the remainder of the book, the authors develop several techniques for constructing exact solutions that describe singularity behavior for various nonlinear PDEs, including gas dynamics models, free-boundary problems, Green-Naghdi equations, and quasilinear pseudo-parabolic (magma) equations. Using exact solutions, they describe the evolution properties related to singularity blow-up or extinction phenomena, finite interface propagation and regularity, and the oscillatory, changing sign behavior of weak solutions near interfaces.

Bestandsnummer des Verkäufers 9780367389970

Bibliografische Details

• Titel: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics
• Verlag: Chapman And Hall/CRC
• Erscheinungsjahr: 2019
• Sprache: Englisch
• ISBN-10: 0367389975
• ISBN-13: 9780367389970
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Galaktionov, Victor A.; Svirshchevskii, Sergey R.