RT info:eu-repo/semantics/article
T1 Parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms
A1 Lastra Sedano, Alberto
A1 Malek, Stephane
K1 Asymptotic expansion
K1 Borel-Laplace transform
K1 Cauchy problem
K1 Difference equation
K1 Integro-differential equation
K1 Linear partial differential equation
K1 Singular perturbation
K1 Matemáticas
K1 Mathematics
AB We consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear fractional transforms. This work is the sequel of a study initiated in [17]. We construct a collection of holomorphic solutions on a full covering by sectors of a neighborhood of the origin in C with respect to the perturbation parameter ϵ. This set is built up through classical and special Laplace transforms along piecewise linear paths of functions which possess exponential or super exponential growth/decay on horizontal strips. A fine structure which entails two levels of Gevrey asymptotics of order 1 and so-called order 1+ is presented. Furthermore, unicity properties regarding the 1+ asymptotic layer are observed and follow from results on summability with respect to a particular strongly regular sequence recently obtained in [13] .
PB Texas State University
SN 1072-6691
YR 2019
FD 2019-04-29
LK http://hdl.handle.net/10017/41510
UL http://hdl.handle.net/10017/41510
LA eng
NO Ministerio de Economía y Competitividad
DS MINDS@UW
RD 27-abr-2024