On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms
Complex Variables
2018-07-20 v1 Analysis of PDEs
Abstract
This paper is a continuation a previous work of the authors where parametric Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied. Here, the partial differential operators are combined with particular Moebius transforms in the time variable. As a result, the leading term of the main problem needs to be regularized by means of a singularly perturbed infinite order formal irregular operator that allows us to construct a set of genuine solutions in the form of a Laplace transform in time and inverse Fourier transform in space. Furthermore, we obtain Gevrey asymptotic expansions for these solutions of some order in the perturbation parameter.
Cite
@article{arxiv.1807.07453,
title = {On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms},
author = {Alberto Lastra and Stéphane Malek},
journal= {arXiv preprint arXiv:1807.07453},
year = {2018}
}