Vladimir A. Marchenko, Evgueni Ya. Khruslov (auth.)0817643516, 9780817643515
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models.
The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory.
Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.
Table of contents :
Front Matter….Pages i-xiii
Introduction….Pages 1-29
The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Fine-Grained Boundary….Pages 31-65
The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Complex Boundary….Pages 67-104
Strongly Connected Domains….Pages 105-135
The Neumann Boundary Value Problems in Strongly Perforated Domains….Pages 137-209
Nonstationary Problems and Spectral Problems….Pages 211-235
Differential Equations with Rapidly Oscillating Coefficients….Pages 237-332
Homogenized Conjugation Conditions….Pages 333-385
Back Matter….Pages 387-398
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