Titlebook: Partial Differential Equations V; Asymptotic Methods f M. V. Fedoryuk Book 1999 Springer-Verlag Berlin Heidelberg 1999 Asymptotic expansion

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,Asymptotic Expansion as , → ∞ of the Solutions of Exterior Boundary Value Problems for Hyperbolic Equations and Quasiclassical Approximations,called simply functions from here on), and . is a (./2) x . matrix of differential operators of order no higher than . — 1. From the conditions . formulated below, it follows that . is even. As a special case, (1) may be a Cauchy problem (this means Ω = ?.).

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The Averaging Method for Partial Differential Equations (Homogenization) and Its Applications,In this paper we consider numerically asymptotic methods for solving partial differential equations with rapidly oscillating periodic coefficients and their application in the solution of a number of problems of mechanics. The paper

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M. V. FedoryukThe authors survey an important topic in PDE which is highly relevant for applications in physics

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978-3-642-63586-1Springer-Verlag Berlin Heidelberg 1999

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Equations with Rapidly Oscillating Solutions,, the equations of elasticity, the Schr?dinger equation, the Dirac equation, and others. There are also nonlinear equations having analogous solutions. Interest in these solutions is becoming immense in theoretical and mathematical physics (the short-wave approximation, the high-frequency approximation, the quasi-classical approximation, etc.).