Long-time asymptotics of solutions of the heat equation

TL;DR

This paper analyzes the long-term behavior of solutions to the heat equation when the initial data exhibits power-law decay at infinity, providing detailed asymptotic descriptions.

Contribution

It develops a method to construct the long-time asymptotics of heat equation solutions with power asymptotic initial conditions.

Findings

Derived explicit asymptotic formulas for solutions

Extended understanding of heat equation behavior with non-compact initial data

Provided a framework for analyzing similar PDEs with power-law decay

Abstract

The long-time asymptotics of solutions of the Cauchy problem for the heat equation are constructed in the case when the initial function at infinity has power asymptotics.