Matching of asymptotic expansions of solutions of boundary value problems. (Согласование асимптотических разложений решений краевых задач.) (Russian. English summary) Zbl 0671.35002

Moskva: Nauka. 336 p. R. 4.30 (1989).
This book is devoted to the “gluing-problems” of different asymptotic expansions of solutions to singularly perturbed boundary value problems for differential equations of different types or in other words to the version of the matching method of gluing of asymptotic expansions in different parameter varying zones that is developed by the author and his colleagues. The topic of the book is considered in monographs for the first time.
The book contains 6 chapters: Functions on the bounding layer of exponential type; Ordinary differential equations; Singular perturbations of domain boundary for elliptic boundary value problems; The elliptic equations with small parameters by derivatives of higher order; Singular perturbations of hyperbolic systems of differential equations; The Cauchy problem for the quasilinear parabolic equations with small parameter.
The main part of the book deals with the different methods and procedures of constructing asymptotic expansions in the whole domain of parameter variation but the justification of the asymptotic expansions considered is given, too.
The book is interesting for both pure mathematicians and specialists in applied problems. The book extends the range of problems considered in the well-known books by M. Van Dyke, A. H. Nayfeh and J. Cole.


35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B25 Singular perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
34D15 Singular perturbations of ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
35J25 Boundary value problems for second-order elliptic equations
35K55 Nonlinear parabolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs