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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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This collection contains papers by participants in the Seminar onMathematical Physics in Kharkov, Ukraine. The papers mainlyfocus on nontraditional problems of spectral theory, such as newtypes of inverse problems for one-dimensional differentialoperators, new classes of solutions to nonlinear differentialequations obtained using spectral methods, distribution ofeigenvalues of large random matrices, and related problems ofstatistical physics of disordered systems. In addition, thepapers explore the spectral aspects of homogenization and ofproperties of ergodic dynamical systems. All the papers containoriginal results published for the first time. ... Read more

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Product Description
This monograph deals with integrable dynamic systems with an infinite number of degrees of freedom. Leading scientists were invited to discuss the notion of integrability with two main points in mind: 1. a presentation of the various recently elaborated methods for determining whether a given system is integrable or not; 2. to understand the increasingly more important role of integrable systems in modern applied mathematics and theoretical physics. Topics dealt with include: the applicability and integrability of "universal" nonlinear wave models (Calogero); perturbation theory for translational invariant nonlinear Hamiltonian systems (in 2+1d) with an additional integral of motion (Zakharov, Schulman); the role of the Painlevé test for ordinary (Ercolani, Siggia) and partial differential (Newell, Tabor) equations; the theory of integrable maps in a plane (Veselov); and the theory of the KdV equation with non-vanishing boundary conditions at infinity (Marchenko). ... Read more