Asymptotic expansions for anisotropic heat kernels

TL;DR

This paper derives asymptotic expansions for solutions of anisotropic heat equations with polynomially weighted initial data, focusing on models with variable diffusivity and the heat equation on the Heisenberg group.

Contribution

It provides new asymptotic expansion formulas for anisotropic heat kernels in complex geometries and variable diffusivity settings.

Findings

Asymptotic expansions for anisotropic heat kernels derived

Results apply to models with variable diffusivity and Heisenberg group

Enhanced understanding of heat propagation in anisotropic media

Abstract

We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity is of order two in some variables but higher in the other ones. In the second one we consider the heat equation on the Heisenberg group.