Swann Marx

L2SN (UMR CNRS 6004) Nantes

27 avril 2023, 14.00
Salle des commissions
Campus St. Jérôme

Singular perturbation analysis for a coupled KdV-ODE system

This talk will be about the singular perturbation analysis of
a Korteweg-de Vries equation, which is a nonlinear PDE modeling waves on
shallow water surfaces, coupled with an ODE. The coupled system may
admit different time-scales, and this particular feature will be taken
into account when analysing the asymptotic stability of the coupled
system. To introduce our methodology, we will first explain how it can
be applied on scalar ODEs. We will then give some insights on the
difficulties when applying it on already known coupled PDE-ODE systems.
Finally, we will show how one can apply this methodology for the KdV-ODE
system under consideration. This talk is based on a joint work with
Eduardo Cerpa, professor at the Universidad Catolica de Chile.