Gradient-like dynamics in a valley and slow motion in nonlinear singularly perturbed PDEs.

Ponente: Peter Bates
Institución: Michigan State University
Tipo de Evento: Investigación

Cuándo	21/04/2022 de 11:00 a 12:00
Dónde	Zoom (liga en la descripción)
Agregar evento al calendario	vCal iCal

The dynamics of a gradient system is obviously determined by the geometric structure (landscape) of the graph of the energy functional. In certain cases, for instance in some singularly perturbed PDE problems, the energy depends on a parameter d and, for 0< d and very small, the graph exhibits special features that have peculiar dynamical counterparts. A quite striking phenomenon in this context is the occurrence of Slow Motion. The geometric structure of the landscape responsible for this phenomenon can qualitatively be described as follows: there exists a manifold M of almost minimal energy in the sense that, in a neighborhood of M, the energy rapidly grows when moving away from M but changes very little along M.

I will give hypotheses that correspond to a quantitative description of the landscape in a neighborhood of M and prove that, provided a certain condition is satisfied, if the initial condition is sufficiently close to M and has energy close to that of typical points on M, then the solution of the gradient system stays near M for a long time or even forever. Thus, a sort of variational maximum principle is manifest.

This is joint work with Giorgio Fusco and Georgia Karali

Liga de Zoom:

https://cuaieed-unam.zoom.us/j/89946525336?pwd=K3FtTytiaVNsZFBBcHlRMjFiVWZFUT09

Meeting ID: 899 4652 5336
Passcode: 570119