# Singularly perturbed linear PDEs associated to several Gevrey level

## Analyse Complexe et Equations Différentielles

Lieu:
Salle Kampé
Orateur:
Alberto Lastra
Dates:
Lundi, 29 Mai, 2017 - 14:00 - 15:00
Résumé:

(joint work with Stéphane Malek)

In the talk, we study the existence of both, formal and analytic solutions associated to a family of singularly perturbed linear PDEs in the complex domain. The link relating these two types of solutions is stated in terms of the so called Borel-Laplace summability method, with respect to the perturbation parameter  $\epsilon$.

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.