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Multi-level Gevrey solutions of singularly perturbed linear partial differential equations
Alberto Lastra,Stéphane Malek +1 more
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In this article, the authors studied the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain, where the analytic solutions obtained by means of a Borel-Laplace summation procedure are represented by a formal power series in the perturbation parameter.Abstract:
We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a Borel-Laplace summation procedure are represented by a formal power series in the perturbation parameter. Indeed, the geometry of the problem gives rise to a decomposition of the formal and analytic solutions so that a multi-level Gevrey order phenomenon appears. This result leans on a Malgrange-Sibuya theorem in several Gevrey levels.read more
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On multiscale Gevrey and Gevrey asymptotics for some linear difference differential initial value Cauchy problems
Alberto Lastra,Stéphane Malek +1 more
TL;DR: In this paper, the authors study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain and prove that the analytic solution can be splitted according to the nature of the equation and its geometry.
Journal ArticleDOI
On Parametric Gevrey Asymptotics for Some Initial Value Problems in Two Asymmetric Complex Time Variables
TL;DR: In this paper, a family of nonlinear initial value problems for partial differential equations in the complex domain under the action of two asymmetric time variables is studied, and different Gevrey bounds and multisummability results are obtained depending on each element of the family.
Posted Content
On parametric Gevrey asymptotics for some nonlinear initial value problems in two complex time variables
Alberto Lastra,Stéphane Malek +1 more
TL;DR: In this article, the asymptotic behavior of singularly perturbed PDEs in two time variables in the complex domain is studied, and the appearance of a multilevel Gevrey phenomenon in the perturbation parameter is observed.
Posted Content
On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables
TL;DR: In this paper, a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables is studied, and different Gevrey bounds and multisummability results are obtained depending on each element of the family.
Journal ArticleDOI
Boundary layer expansions for initial value problems with two complex time variables
Alberto Lastra,Stéphane Malek +1 more
TL;DR: In this paper, a family of partial differential equations in the complex domain under the action of a complex perturbation parameter ϵ was studied, and inner and outer solutions of the problem were derived via Gevrey asymptotic expansions with respect to ϵ in adequate domains.
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