Asymptotic expansions of fundamental solutions in parabolic homogenization

Geng, Jun; Shen, Zhongwei

doi:10.2140/apde.2020.13.147

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Asymptotic expansions of fundamental solutions in parabolic homogenization

Jun Geng and Zhongwei Shen

Vol. 13 (2020), No. 1, 147–170

DOI: 10.2140/apde.2020.13.147

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

Vol. 13, No. 1, 2020