On a q-analog of a singularly perturbed problem of irregular type with two complex time variables
The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/41509 |
| Acceso en línea: | http://hdl.handle.net/10017/41509 https://dx.doi.org/10.3390/math7100924 |
| Access Level: | acceso abierto |
| Palabra clave: | Asymptotic expansion Borel-Laplace transform Fourier transform Initial value problem Formal power series q-difference equation Boundary layer Singular perturbation Matemáticas Mathematics |
| Sumario: | The analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain are constructed and studied from an asymptotic point of view with respect to the perturbation parameter. Two types of holomorphic solutions, the so-called inner and outer solutions, are considered. Each of them holds a particular asymptotic relation with the formal ones in terms of asymptotic expansions in the perturbation parameter. The growth rate in the asymptotics leans on the --1-branch of Lambert W function, which turns out to be crucial. |
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