Vol. 13, No. 1, 2020

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Asymptotic expansions of fundamental solutions in parabolic homogenization

Jun Geng and Zhongwei Shen

Vol. 13 (2020), No. 1, 147–170
Abstract

For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.

Keywords
homogenization, parabolic system, fundamental solution
Mathematical Subject Classification 2010
Primary: 35B27, 35E05, 35K40
Milestones
Received: 1 January 2018
Revised: 28 October 2018
Accepted: 29 December 2018
Published: 6 January 2020
Authors
Jun Geng
School of Mathematics and Statistics
Lanzhou University
Lanzhou
China
Zhongwei Shen
Department of Mathematics
University of Kentucky
Lexington, KY
United States