2019/01/16 by Alberto Lastra, Lastra, Alberto, Stéphane Malek +2
Mathematics · #35C10 #35C15 #35C20 #35R10 #Analysis of PDEs (math.AP) #Cauchy distribution #Complex Variables (math.CV) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Gravitational singularity #Holomorphic function #Initial value problem #Iterated function #Laplace transform #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Nonlinear system #Physics #Pure mathematics #Singularity #math.AP #math.CV #msc:35C10 #msc:35C15 #msc:35C20 #msc:35R10
paper · pdf · doi:10.48550/arxiv.1901.05210
arxiv created 2019/01/16 · openalex publication_date 2019/01/16 · arxiv updated 2019/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a family of linear singularly perturbed PDE relying on a complex\nperturbation parameter \ε. As in a former study of the authors (A.\nLastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial\nvalue Cauchy problems, J. Differential Equations 259 (2015), no. 10,\n5220--5270), our problem possesses an irregular singularity in time located at\nthe origin but, in the present work, it entangles also differential operators\nof Fuchsian type acting on the time variable. As a new feature, a set of\nsectorial holomorphic solutions are built up through iterated Laplace\ntransforms and Fourier inverse integrals following a classical multisummability\nprocedure introduced by W. Balser. This construction has a direct issue on the\nGevrey bounds of their asymptotic expansions w.r.t \ε which are shown\nto bank on the order of the leading term which combines both irregular and\nFuchsian types operators.\n