[内容简介]
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 hardly been examined so far in the literature dedicated to singular perturbations. This book proposes to fill in 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 mathematical models
The book covers mostly original results by the authors. It is designed for researchers and graduate students. [目次]
Preface.
- I Preliminaries.
- 1. Regular and Singular Perturbations.
- 2. Evolution Equations in Hilbert Spaces.
-II Singularly Perturbed Hyperbolic Problems.
- 3. Presentation of the Problems.
- 4. Hyperbolic Systems with Algebraic Boundary Conditions.
- 5. Hyperbolic Systems with Dynamic Boundary Conditions.
- III Singularly Perturbed Coupled Boundary Value Problems.
- 6. Presentation of the Problems.
- 7. The Stationary Case.
- 8. The Evolutionary Case.- IV Elliptic and Hyperbolic Regularizations of Parabolic Problems.
- 9. Presentation of the Problems.
- 10. The Linear Case.
- 11. The Nonlinear Case.