Spectral approach to homogenization of hyperbolic equations with periodic coefficients

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Dorodnyi, M. A.¹  Suslina, T. A.¹ 

[1] St Petersburg State Univ, Univ Skaya Nab 7-9, St Petersburg 199034, Russia

关键词: Periodic differential operators;    Hyperbolic equations;    Homogenization;    Effective operator;    Operator error estimates;   

DOI  :  10.1016/j.jde.2018.02.023

来源: Elsevier

【 摘 要 】

In L-2 (R-d; C-n), we consider selfadjoint strongly elliptic second order differential operators A(epsilon) with periodic coefficients depending on x/epsilon, epsilon > 0. We study the behavior of the operators cos(A(epsilon)(1/2)tau) and A(epsilon)(-1/2) sin(A(epsilon)(1/2)tau), tau is an element of R, for small epsilon. Approximations for these operators in the (H-s -> L-2)-operator norm with a suitable s are obtained. The results are used to study the behavior of the solution v(epsilon) of the Cauchy problem for the hyperbolic equation partial derivative(2)(tau)v(epsilon) = -A(epsilon)v(epsilon) + F. General results are applied to the acoustics equation and the system of elasticity theory. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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