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

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 $\epsilon$ 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.

References in corpus (3)

• An extension of Borel-Laplace methods and monomial summability
• Tauberian properties for monomial summability with applications to Pfaffian systems
• Multi-level Gevrey solutions of singularly perturbed linear partial differential equations

Cited by in corpus (1)

• On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables