Theory and Applications of Partial Functional Differential Equations

By: Jianhong Wu

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Hardcover | 26 September 1996

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448 Pages

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24.77 x 17.15 x 3.18

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This book provides an introduction to the qualitative theory and applications of partial functional differential equations from the viewpoint of dynamical systems. Many fundamental results and methods scattered throughout research journals are described, various applications to population growth in a heterogeneous environment are presented and a comprehensive bibliography from both mathematical and biological sources is provided. The main emphasis of the book is on reaction-diffusion equations with delayed nonlinear reaction terms and on the joint effect of the time delay and spatial diffusion on the spatial-temporal patterns of the considered systems. The presentation is self-contained and accessible to the nonspecialist. The book should be of value to graduate students and researchers in dynamical systems, differential equations, semigroup theory, nonlinear analysis and mathematical biology. The style of the presentation appeals especially to people trained and interested in the qualitative theory of ordinary/functional/partial differential equations.

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Preface
Introduction	p. 1
Preliminaries	p. 20
Existence and Compactness of Solution Semiflows	p. 36
Generators and Decomposition of State Spaces for Linear Systems	p. 65
Nonhomogeneous Systems and Linearized Stability	p. 111
Invariant Manifolds of Nonlinear Systems	p. 143
Hopf Bifurcations	p. 182
Small and Large Diffusivity	p. 241
Invariance, Comparison, and Upper and Lower Solutions	p. 268
Convergence, Monotonicity, and Contracting Rectangles	p. 295
Dispativeness, Exponential Growth, and Invariance Principles	p. 323
Traveling Wave Solutions	p. 349
Bibliography	p. 400
Index	p. 427
Table of Contents provided by Blackwell. All Rights Reserved.

Theory and Applications of Partial Functional Differential Equations

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Hardcover

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