Asymptotic Expansions of Fundamental Solutions in Parabolic Homogenization

TL;DR

This paper studies the long-term behavior of fundamental solutions in parabolic systems with rapidly oscillating, time-dependent periodic coefficients, providing precise estimates for the approximation errors.

Contribution

It introduces new asymptotic expansions and sharp estimates for fundamental solutions in parabolic homogenization with time-dependent coefficients.

Findings

Established asymptotic expansions for fundamental solutions.

Derived sharp estimates for remainders in the expansions.

Enhanced understanding of parabolic homogenization with time-dependent coefficients.

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.