Ebook: Theory and Applications of Partial Functional Differential Equations

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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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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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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-19
Preliminaries....Pages 20-35
Existence and Compactness of Solution Semiflows....Pages 36-64
Generators and Decomposition of State Spaces for Linear Systems....Pages 65-110
Nonhomogeneous Systems and Linearized Stability....Pages 111-142
Invariant Manifolds of Nonlinear Systems....Pages 143-181
Hopf Bifurcations....Pages 182-243
Small and Large Diffusivity....Pages 244-267
Invariance, Comparison, and Upper and Lower Solutions....Pages 268-294
Convergence, Monotonicity, and Contracting Rectangles....Pages 295-322
Dispativeness, Exponential Growth, and Invariance Principles....Pages 323-348
Traveling Wave Solutions....Pages 349-399
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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-19
Preliminaries....Pages 20-35
Existence and Compactness of Solution Semiflows....Pages 36-64
Generators and Decomposition of State Spaces for Linear Systems....Pages 65-110
Nonhomogeneous Systems and Linearized Stability....Pages 111-142
Invariant Manifolds of Nonlinear Systems....Pages 143-181
Hopf Bifurcations....Pages 182-243
Small and Large Diffusivity....Pages 244-267
Invariance, Comparison, and Upper and Lower Solutions....Pages 268-294
Convergence, Monotonicity, and Contracting Rectangles....Pages 295-322
Dispativeness, Exponential Growth, and Invariance Principles....Pages 323-348
Traveling Wave Solutions....Pages 349-399
Back Matter....Pages 400-432
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