Alberto Lastra, Stephane Malek
Multiscale Gevrey asymptotics in boundary layer expansions for some initial value problem with merging turning points
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ABSTRACT. We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter. The problem possesses an irregular singularity in time at the origin and involves a set of so-called
moving turning points merging to 0 with the perturbation parameter. We construct outer solutions for time located in
complex sectors that are kept away from the origin at a distance equivalent to a positive power of the parameter and we
build up a related family of sectorial holomorphic inner solutions for small time inside some boundary layer. We show that both outer and inner solutions have Gevrey asymptotic expansions as the parameter tends to 0 on appropriate sets of sectors that cover a neighborhood of the origin in the complex domain. We observe that their Gevrey orders are distinct in general.