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

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 sm...

Descripción completa

Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane, Chen, Guoting
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/44947
Acceso en línea:http://hdl.handle.net/10017/44947
https://dx.doi.org/10.1186/s13662-020-02773-z
Access Level:acceso abierto
Palabra clave:Asymptotic expansion
Borel-Laplace transform
Fourier transform
Initial value problem
Formal power series
Nonlinear partial differential equation
Singular perturbation
Matemáticas
Mathematics
Descripción
Sumario: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.