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...

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Detalles Bibliográficos
Autores: Lastra Sedano, Alberto|||0000-0002-4012-6471, Malek, Stephane
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
Descripción
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.