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"The aim of homogenization theory is to establish the macroscopic behaviour of a microinhomogenous system, in order to describe some characteristics of the given heterogeneous medium. a ] The book is an excellent, practice oriented, and well written introduction to homogenization theory bringing the reader to the frontier of current research in the area. It is highly recommended to graduate students in applied mathematics as well as to researchers interested in mathematical modeling and asymptotical analysis." (J. Kolumban, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)
Product Description
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.
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strongly perforated domains, small inclusions, elastic plates, strong connectivity condition, function whs, mean conductivity tensor, microinhomogeneous medium, function minimizing the functional, connectedness matrix, homogenized model, conjugation conditions, weak connectedness, lim mes, oscillating coefficients, homogenized equation, yellow nodes, model with memory, blue nodes, following initial boundary value problem, conormal derivative, green nodes, conjugation problem, nonstationary problems, following boundary value problem, extension condition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Differential Equations, The Neumann Boundary Value Problems, Rapidly Oscillating Coefficients, The Dirichlet Boundary Value Problem, Homogenized Conjugation Conditions, Complex Boundary, High Heat Capacity Inclusions, Surface Distribution of Sets, Applying Lemma, Homogenized Diffusion Model, Surface Distribution of Inclusions, The Neumann Problem, Random Fine-Grained Boundary, Method of Orthogonal Projections, Stationary Josephson Effect, Weakly Nonlinear Medium, Preliminary Considerations, Electrostatic Field, Periodic Structures, Nonlocal Homogenized Model, Strongly Connected Domains, Weakly Connected Domains New!
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