The Stokes phenomenon for certain partial differential equations with variable coefficients depending on the time variable

TL;DR

This paper investigates the Stokes phenomenon in solutions to certain PDEs with time-dependent variable coefficients, employing summability and hyperfunction theories to analyze Stokes lines and jumps.

Contribution

It introduces a novel application of summability and hyperfunction methods to describe Stokes phenomena in PDEs with variable coefficients depending on time.

Findings

Identification of Stokes lines and jumps in PDE solutions

Application of hyperfunction theory to analyze Stokes phenomena

Extension of summability methods to PDEs with variable coefficients

Abstract

We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of hyperfunctions to describe Stokes lines and jumps across these Stokes lines.