This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for 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 treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations.

Preliminaries.- Regular and Singular Perturbations.- Evolution Equations in Hilbert Spaces.- Singularly Perturbed Hyperbolic Problems.- Presentation of the Problems.- Hyperbolic Systems with Algebraic Boundary Conditions.- Hyperbolic Systems with Dynamic Boundary Conditions.- Singularly Perturbed Coupled Boundary Value Problems.- Presentation of the Problems.- The Stationary Case.- The Evolutionary Case.- Elliptic and Hyperbolic Regularizations of Parabolic Problems.- Presentation of the Problems.- The Linear Case.- The Nonlinear Case.