GSPT for Fast-Slow PDEs (C. Kühn, TUM)
Datum: 04-02-2022Zeit: 11:30 – 12:30Ort: Online
GSPT for Fast-Slow PDEs
Speaker: Prof. Dr. Christian Kühn
Affiliation: TU München, Germany,
Website: http://www.multiscale.systems/index.html
Zoom link: https://fau.zoom.us/j/5308678850?pwd=V1JvOEVIc1VwU1U4Vi9PUHAwM0FTZz09
Meeting ID: 530 867 8850, PIN: 014005
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.
Details
Online