On parametric Gevrey asymptotics for some nonlinear initial value problems in symmetric complex time variables

Article type: Research Article

Authors: Lastra, A.^{a; *} | Malek, S.^b

Affiliations: [a] Departamento de Física y Matemáticas, University of Alcalá, Ap. de Correos 20, E-28871 Alcalá de Henares (Madrid), Spain. E-mail: alberto.lastra@uah.es | [b] Laboratoire Paul Painlevé, University of Lille 1, 59655 Villeneuve d’Ascq cedex, France. E-mail: Stephane.Malek@math.univ-lille1.fr

Correspondence: [*] Corresponding author. E-mail: alberto.lastra@uah.es.

Abstract: The asymptotic behavior of a family of singularly perturbed PDEs in two time variables in the complex domain is studied. The appearance of a multilevel Gevrey asymptotics phenomenon in the perturbation parameter is observed. We construct a family of analytic sectorial solutions in ϵ which share a common asymptotic expansion at the origin, in different Gevrey levels. Such orders are produced by the action of the two independent time variables.

Keywords: Asymptotic expansion, Borel–Laplace transform, Fourier transform, initial value problem, formal power series, nonlinear integro-differential equation, nonlinear partial differential equation, singular perturbation

DOI: 10.3233/ASY-191568

Journal: Asymptotic Analysis, vol. 118, no. 1-2, pp. 49-79, 2020