2018/07/19 by Alberto Lastra, Lastra, Alberto, Stéphane Malek +1
Engineering · Mathematics · #35C10 #35C15 #35C20 #35R10 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics #math.AP #math.CV #msc:35C10 #msc:35C15 #msc:35C20 #msc:35R10
paper · pdf · doi:10.48550/arxiv.1807.07453
arxiv created 2018/07/19 · openalex publication_date 2018/07/19 · arxiv updated 2018/07/20 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
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 K>1 in the perturbation parameter.