Boundary layer expansions for initial value problems with two complex time variables

Advances in Difference Equations

article

Lastra, A.¹  Malek, S.² 

[1] 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;    Boundary layer;    Singular perturbation;   

DOI  :  10.1186/s13662-020-2496-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis–Sibuya theorem.

【 授权许可】

CC BY