RT info:eu-repo/semantics/article
T1 On parametric Gevrey asymptotics for initial value  problems with infinite order irregular singularity and linear fractional  transforms
A1 Lastra Sedano, Alberto
A1 Malek, Stephane
K1 Asymptotic expansion
K1 Borel-Laplace transform
K1 Fourier transform
K1 Initial value problem
K1 Difference equation
K1 Formal power series
K1 Nonlinear integro-differential equation
K1 Nonlinear partial differential equation
K1 Singular perturbation
K1 Matemáticas
K1 Mathematics
AB This paper is a continuation of the work (Lastra and Malek in J. Differ. Equ. 259(10):5220-5270, 2015) where singularly perturbed nonlinear PDEs have been studied from an asymptotic point of view. 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 an inverse Fourier transform in space. Furthermore, we obtain Gevrey asymptotic expansions for these solutions of some order K > 1 in the perturbation parameter.
PB Springer Open
SN 1687-1839
YR 2018
FD 2018-10-23
LK http://hdl.handle.net/10017/41476
UL http://hdl.handle.net/10017/41476
LA eng
NO Ministerio de Economía y Competitividad
DS MINDS@UW
RD 02-may-2024