Alberto Lastra, Stephane Malek
We consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear fractional transforms. This work is the sequel of a study initiated in . We construct a collection of holomorphic solutions on a full covering by sectors of a neighborhood of the origin in with respect to the perturbation parameter . This set is built up through classical and special Laplace transforms along piecewise linear paths of functions which possess exponential or super exponential growth/decay on horizontal strips. A fine structure which entails two levels of Gevrey asymptotics of order 1 and so-called order is presented. Furthermore, unicity properties regarding the asymptotic layer are observed and follow from results on summability with respect to a particular strongly regular sequence recently obtained in .
Submitted April 20, 2018. Published April 29, 2019.
Math Subject Classifications: 35R10, 35C10, 35C15, 35C20.
Key Words: Asymptotic expansion; Borel-Laplace transform; Cauchy problem; difference equation; integro-differential equation; linear partial differential equation; singular perturbation.
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| Alberto Lastra |
Dpto. de Física y Matemáticas
Universidad de Alcalá, Ap. Correos 20
E-28871 Alcalá de Henares, Madrid, Spain
| Stephane Malek |
University of Lille 1, Laboratoire Paul Painlevé
59655 Villeneuve d'Ascq cedex, France
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