The Stokes phenomenon for certain partial differential equations with meromorphic initial data
S{\l}awomir Michalik, Bo\.zena Podhajecka
TL;DR
This paper investigates the Stokes phenomenon in solutions to the 1D complex heat equation with meromorphic initial data, using Borel summability to analyze Stokes lines, jumps, and solution families.
Contribution
It introduces a Borel summability framework to describe the Stokes phenomenon for complex heat equations with meromorphic initial data, extending existing analysis methods.
Findings
Characterization of Stokes and anti-Stokes lines
Description of jumps across Stokes lines
Construction of the maximal family of solutions
Abstract
We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of the Stokes lines, the anti-Stokes lines, jumps across the Stokes lines, and the maximal family of the solutions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.