The Stokes phenomenon for certain PDEs in a case when initial data have a finite set of singular points

TL;DR

This paper investigates the Stokes phenomenon for solutions to a 1D complex heat equation with initial data having finitely many singular points, using hyperfunctions and summability theory to describe Stokes line jumps.

Contribution

It introduces a novel approach combining hyperfunctions and summability to analyze Stokes phenomena with finitely many singular initial data points.

Findings

Describes jumps across Stokes lines using hyperfunctions.

Provides a framework for analyzing PDEs with singular initial data.

Extends understanding of Stokes phenomena in complex heat equations.

Abstract

We study the Stokes phenomenon via hyperfunctions for the solutions of the 1-dimensional complex heat equation under the condition that the Cauchy data are holomorphic on $\mathbb{C}$ but a finitely many singular or branching points with the appropriate growth condition at the infinity. The main tool are the theory of summability and the theory of hyperfunctions, which allows us to describe jumps across Stokes lines.