The Stokes phenomenon for some moment partial differential equations

Abstract

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex plane but finitely many singular or branching points with the appropriate growth condition at the infinity. The main tools are the theory of summability and multisummability, and the theory of hyperfunctions. Using them we describe Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a maximal family of solutions.

arXiv comment21 pages

References in corpus (3)

• Summability of formal solutions of linear partial differential equations with divergent initial data
• Analytic and summable solutions of inhomogeneous moment partial differential equations
• The Stokes phenomenon for certain partial differential equations with meromorphic initial data

Cited by in corpus (3)

• Estimates of formal solutions for some generalized moment partial differential equations
• Summability of formal solutions for a family of generalized moment integro-differential equations
• Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations