The Boundary Function Method for Singular Perturbation Problems

1. Basic Ideas; Regular and singular perturbations; Asymptotic approximations; Asymptotic and convergent series; Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems; 2. Singularly perturbed ordinary differential equations; Initial value problem; The critical case; Boundary value problems; Spike-type solutions and other contrast (dissipative) structures; 3. Singularly perturbed partial differential equations; The method of Vishik-Lyusternik; Corner boundary functions; The smoothing procedure; Systems of equations in critical cases; Periodic solutions; Hyperbolic systems; 4. Applied problems; Mathematical model of combustion process in the case of autocatalytic reaction; Heat conduction in thin Bodies; Application of the boundary function method in the theory of semiconductor devices; Relaxation waves in the FitzHugh-Nagumo system; On some other applied problems; Index.