UniversityNews & EventsEvents
Global Stability for a Thermostat Model
22 Oct
22. October 2019
Oberseminar Analysis und Theoretische Physik

Global Stability for a Thermostat Model

The global asymptotic stability of the unique steady state of a nonlinear scalar diffusion equation with a nonlocal boundary condition is studied. The equation describes the evolution of a temperature profile that is subject to a feedback control loop. It can be viewed as a model for a rudimentary thermostat, where a parameter controls the intensity of the heat flow in response to the magnitude of the deviation from the reference temperature at a boundary point. The system is known to undergo a Hopf bifurcation when the parameter exceeds a critical value. Results on the characterization of the maximal parameter range where the reference steady state is globally asymptotically stable are obtained by analyzing a closely related nonlinear Volterra integral equation. Its kernel is derived from the trace of a fundamental solution of a linear heat equation. A version of the Popov criterion is adapted and applied to the Volterra integral equation to obtain a sufficient condition for the asymptotic decay of its solutions

Speaker

Prof. Dr. Patrick Guidotti (University of California - Irvine)

Organiser

Institut für Angewandte Mathematik

Date

22. October 2019
15:00 o'clock - 16:30 o'clock

Public contact

Antje Günther
Institut für Angewandte Mathematik
Welfengarten 1
30167 Hannover
Tel.: 0511/762-3251
Fax: 0511/762-3988
guenther@ifam.uni-hannover.de

Location

Leibniz Universität Hannover
Building: 1101
Room: c311
Welfengarten 1
30167 Hannover
show on map

Url