Theory and Applications of Partial Functional Differential Equations

Hardcover | September 26, 1996

byJianhong Wu

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Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

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From Our Editors

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 prese...

From the Publisher

Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations fr...

Format:HardcoverDimensions:442 pages, 9.25 × 6.1 × 0.03 inPublished:September 26, 1996Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:038794771X

ISBN - 13:9780387947716

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Table of Contents

Contents: Introduction.- Preliminaries.- Existence and compactness of solution semiflows. Generators and decomposition of state spaces for linear systems.- Nonhomogenous systems and linearized stability.- Invariant manifolds of nonlinear systems.- Hopf Bifurcations.- Small and large diffusivity.- Invariance, comparison, lower and upper solutions.- Convergence, monotononicity and contracting rectangles.- Dispativeness, exponential growth and invariance principles.- Travelling wave solutions.- References.- Index.

From Our Editors

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.