Hyperasymptotic solutions for certain partial differential equations

TL;DR

This paper develops hyperasymptotic expansions for solutions of the heat equation and extends the approach to general linear PDEs with constant coefficients using Borel summability.

Contribution

It introduces a method to obtain hyperasymptotic solutions for linear PDEs with constant coefficients via Borel summability, generalizing previous results.

Findings

Derived hyperasymptotic expansions for heat equation solutions

Extended the method to general linear PDEs with constant coefficients

Provided integral representations of solutions using Borel summability

Abstract

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.