GSPT for Fast-Slow PDEs (C. Kühn, TUM)

Feb 04
04-02-2022 11:30 Uhr bis 12:30 Uhr
Online

GSPT for Fast-Slow PDEs

Speaker: Prof. Dr. Christian Kühn
Affiliation: TU München, Germany,
Website: ttp://www.multiscale.systems/index.html

Zoom link: https://fau.zoom.u
Meeting ID: , Passcode:

Abstract: Systems with multiple time scales appear in a wide variety of
applications. Yet, their mathematical analysis is challenging already in
the context of ordinary differential equations (ODEs), where about four
decades were needed to develop a more comprehensive theory based upon
invariant manifolds, desingularization, variational equations, and many
other techniques. This framework has become known as geometric singular
perturbation theory (GSPT). Yet, for partial differential equations
(PDEs) progress has been extremely slow due to many obstacles in
generalizing several ODE methods. In my talk, I shall report on two
recent advances for fast-slow PDEs, namely the extension of slow
manifold theory for unbounded operators driving the slow variables, and
the design of a blow-up method for PDEs, where normal hyperbolicity is
lost. This is joint work with Maximilian Engel and Felix Hummel.

https://dcn.nat.fau.eu

Friedrich-Alexander-Universität Erlangen-Nürnberg