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
Referent/Referentin
Prof. Dr. Patrick Guidotti (University of California - Irvine)
Veranstalter
Institut für Angewandte Mathematik
Termin
22. Oktober 201915:00 Uhr - 16:30 Uhr
Kontakt
Antje GüntherInstitut für Angewandte Mathematik
Welfengarten 1
30167 Hannover
Tel.: 0511/762-3251
Fax: 0511/762-3988
guenther@ifam.uni-hannover.de
Ort
Leibniz Universität HannoverGeb.: 1101
Raum: c311
Welfengarten 1
30167 Hannover