Theory and Applications of Partial Functional Differential Equations

1. Front Matter

   Pages i-x

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2. Introduction

   • Jianhong Wu

   Pages 1-19

3. Preliminaries

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   Pages 20-35

4. Existence and Compactness of Solution Semiflows

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   Pages 36-64

5. Generators and Decomposition of State Spaces for Linear Systems

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   Pages 65-110

6. Nonhomogeneous Systems and Linearized Stability

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   Pages 111-142

7. Invariant Manifolds of Nonlinear Systems

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   Pages 143-181

8. Hopf Bifurcations

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   Pages 182-243

9. Small and Large Diffusivity

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   Pages 244-267

10. Invariance, Comparison, and Upper and Lower Solutions

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    Pages 268-294

11. Convergence, Monotonicity, and Contracting Rectangles

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    Pages 295-322

12. Dispativeness, Exponential Growth, and Invariance Principles

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    Pages 323-348

13. Traveling Wave Solutions

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    Pages 349-399

14. Back Matter

    Pages 400-432

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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.

• compactness
• differential equation
• manifold
• maximum
• wave equation

• Department of Mathematics and Statistics, York University, North York, Canada

  Jianhong Wu

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