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...
| Autores: | , , |
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| 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 |
| 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. |
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