[Author]
 Dorodnyi, M. A.

[Title]
 High-frequency homogenization of multidimensional hyperbolic equations

[AMS Subj-class]
 35B27 Homogenization; partial differential equations in media with periodic structure

[Keywords]
 periodic differential operators, hyperbolic equations, spectral bands,
 homogenization, effective operator, operator error estimates

[Abstract]
 In $L_2(\mathbb{R}^d)$, we consider an elliptic differential operator
 $\mathcal{A}_\varepsilon = - \operatorname{div} g(\mathbf{x}/\varepsilon) \nabla + 
 \varepsilon^{-2} V(\mathbf{x}/\varepsilon)$, $ \varepsilon > 0$, with periodic 
 coefficients. For hyperbolic equations with the operator $\mathcal{A}_\varepsilon$,
 analogs of homogenization problems related to an arbitrary point of 
 the dispersion relation of the operator $\mathcal{A}_1$ are studied 
 (the so called high-frequency homogenization). For the solutions of the Cauchy 
 problems for these equations with special initial data, approximations in 
 $L_2(\mathbb{R}^d)$-norm for small $\varepsilon$ are obtained.

[Comments]
 Russian, 44 pp.

[Contact e-mail]
 mdorodni@yandex.ru