Convergence rates in homogenization of higher-order parabolic systems

Weisheng Niu; Yao Xu

doi:10.3934/dcds.2018183

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2018, Volume 38, Issue 8: 4203-4229. Doi: 10.3934/dcds.2018183

This issue Previous Article Bifurcation of limit cycles for a family of perturbed Kukles differential systems Next Article Second order regularity for degenerate nonlinear elliptic equations

Convergence rates in homogenization of higher-order parabolic systems

Weisheng Niu^1, and
Yao Xu^2, ,

1.
School of Mathematical Science, Anhui University, Hefei 230601, China
2.
Department of Mathematics, Nanjing University, Nanjing 210093, China

^* Corresponding author: Yao Xu
^* Corresponding author: Yao Xu

Received: December 31, 2017

Published: May 2018

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Abstract

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 [25] is used here.

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Mathematics Subject Classification: Primary: 35B27; Secondary: 35K52.

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