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

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