Multiscale Gevrey asymptotics in boundary layer expansions for some initial value problem with merging turning points [article]

Alberto Lastra, Stéphane Malek
2017 arXiv   pre-print
We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter ϵ. 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 ϵ. 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 |ϵ| and we build up a related family of sectorial holomorphic inner solutions for small time inside some
more » ... y layer. We show that both outer and inner solutions have Gevrey asymptotic expansions as ϵ tends to 0 on appropriate sets of sectors that cover a neighborhood of the origin in C^∗. We observe that their Gevrey orders are distinct in general.
arXiv:1707.02323v1 fatcat:7hkv37pi5rfotjwbsgus3zm5ym