Singularly Perturbed Boundary-Value Problems

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