This book deals with the solution of singularly perturbed boundary value problems for differential equations. It presents, for the first time, a detailed and systematic treatment of the version of the matching method developed by the author and his colleagues. A broad class of problems is considered from a unified point of view, and the procedure for constructing asymptotic expansions is discussed in detail. The book covers formal constructions of asymptotic expansions and provides rigorous justifications of these asymptotics. One highlight is a complete asymptotic analysis of Burger's equation with small diffusion in the neighborhood of the gradient catastrophe point. The book is suitable as a text for graduate study in asymptotic methods in calculus and singularly perturbed equations.

Readership

Graduate students and researchers specializing in differential equations.

Reviews

"A valuable reference book."

-- Bulletin of the London Mathematical Society

Table of Contents

• Boundary layer functions of exponential type
• Ordinary differential equations
• Singular perturbations of the domain boundary in elliptic boundary value problems
• Elliptic equation with small parameter at higher derivatives
• Singular perturbation of a hyperbolic system of equations
• Cauchy problem for quasilinear parabolic equation with a small parameter