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Convergence rates in homogenization of higher-order parabolic systems. (English) Zbl 1403.35037

Summary: This paper is concerned with the optimal convergence rate in homogenization of higher order parabolic systems with bounded measurable, rapidly oscillating periodic coefficients. The sharp \(O(\varepsilon)\) convergence rate in the space \(L^2(0, T; H^{m-1}(\Omega))\) is obtained for both the initial-Dirichlet problem and the initial-Neumann problem. The duality argument inspired by T. A. Suslina [Mathematika 59, No. 2, 463–476 (2013; Zbl 1272.35021)] is used here.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K52 Initial-boundary value problems for higher-order parabolic systems

Citations:

Zbl 1272.35021
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References:

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