Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms

Advances in Difference Equations

article

Chen, G.¹  Lastra, A.²  Malek, S.³ 

[1] Harbin Institute of Technology (Shenzhen);Departamento de Física y Matemáticas, University of Alcalá;Laboratoire Paul Painlevé, University of Lille 1

关键词: Asymptotic expansion;    Borel–Laplace transform;    Fourier transform;    Initial value problem;    Formal power series;    Nonlinear partial differential equation;    Singular perturbation;   

DOI  :  10.1186/s13662-020-02773-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows one to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work (Lastra and Malek in Adv. Differ. Equ. 2020:20, 2020) by the last two authors. The result leans on the application of a fixed point argument and the classical Ramis–Sibuya theorem.

【 授权许可】

CC BY