Bifurcation Theory And Applications

By: Shouhong Wang, Tian Ma

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Hardcover | 28 June 2005

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392 Pages

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23.4 x 15.9 x 2.7

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This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.

Industry Reviews

The book provides a nice introduction to a variety of bifurcation problems ]] -- Mathematical Reviews "Mathematical Reviews"

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics Chaos Theory Science Physics Classical Mathematics Fluid Mechanics Nonlinear Science Booktopia Publisher Services

World Scientific Publishing

Introduction to steady state bifurcation theory	p. 1
Introduction to dynamic bifurcation	p. 21
Reduction procedures and stability	p. 41
Steady state bifurcations	p. 75
Dynamic bifurcation theory : finite dimensional case	p. 105
Dynamic bifurcation theory : infinite dimensional case	p. 151
Bifurcations for nonlinear elliptic equations	p. 197
Reaction-diffusion equations	p. 241
Pattern formation and wave equations	p. 267
Fluid dynamics	p. 327
Table of Contents provided by Blackwell. All Rights Reserved.

Bifurcation Theory And Applications

At a Glance

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Industry Reviews

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Defective items

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