Includes bibliographical references (p. 251-253) and indexes.
Uniform asymptotic formulae for Green's functions for the laplacian in domains with small perforations
Mixed and Neumann boundary conditions for domains with small holes and inclusions: Uniform asymptotics of Green's kernels
Green's function for the Dirichlet boundary value problem in a domain with several inclusions
Numerical simulations based on the asymptotic approximations
Other examples of asymptotic approximations of Green's functions in singularly perturbed domains
Green's tensor of the Dirichlet boundary value problem in a domain with a single inclusion
Green's tensor in bodies with multiple rigid inclusions
Green's tensor for the mixed boundary value problem in a domain with a small hole
Meso-scale approximations for solutions of Dirichlet problems
Mixed boundary value problems in multiply-perforated domains.
The main focus of the present text is on two topics: (a) asymptotics of Green's kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.