Singularly Perturbed Boundary-Value Problems

Luminiţa Barbu, Gheorghe Moroşanu (auth.)3764383305, 9783764383305

This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for various phenomena in biology, chemistry, and engineering.

The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The book fills this gap, since most applications are described by nonlinear models. Their asymptotic analysis is very interesting, but requires special methods and tools. The treatment presented in this volume combines some of the most successful results from different parts of mathematics, including functional analysis, singular perturbation theory, partial differential equations, and evolution equations. Thus a complete justification for the replacement of various perturbed models with corresponding reduced models, which are simpler but in general have a different character, is offered to the reader.

Specific applications are addressed, such as propagation of electromagnetic or mechanical waves, fluid flows, or diffusion processes. However, the methods presented are also applicable to other mathematic

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Table of contents :
Front Matter….Pages i-xiii
Front Matter….Pages 1-1
Regular and Singular Perturbations….Pages 3-15
Evolution Equations in Hilbert Spaces….Pages 17-34
Front Matter….Pages 35-35
Presentation of the Problems….Pages 37-41
Hyperbolic Systems with Algebraic Boundary Conditions….Pages 43-64
Hyperbolic Systems with Dynamic Boundary Conditions….Pages 65-110
Front Matter….Pages 111-111
Presentation of the Problems….Pages 113-116
The Stationary Case….Pages 117-142
The Evolutionary Case….Pages 143-177
Front Matter….Pages 179-179
Presentation of the Problems….Pages 181-183
The Linear Case….Pages 185-208
The Nonlinear Case….Pages 209-226
Back Matter….Pages 227-231