The Stokes phenomenon for certain partial differential equations with meromorphic initial data

Article type: Research Article

Authors: Michalik, Sławomir^{; *} | Podhajecka, Bożena

Affiliations: Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938 Warszawa, Poland

Correspondence: [*] Corresponding author. E-mail: s.michalik@uksw.edu.pl; URL: http://www.impan.pl/~slawek.

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 Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a maximal family of the solutions.

Keywords: Stokes phenomenon, heat equation, Borel summability

DOI: 10.3233/ASY-161379

Journal: Asymptotic Analysis, vol. 99, no. 3-4, pp. 163-182, 2016