Kolloquien und Oberseminare Übersicht Detail

Speaker:
Manuel Rissel (Shanghai Jiao Tong University)

Zoom link for this talk.

This talk is concerned with exponential stability for solutions to a linear transmission problem in one spatial dimension modeling the evolution of an elastic-thermoelastic-elastic bar. The thermoelastic middle part of the bar is subject to either Cattaneo’s- or Fourier’s law for heat conduction while the elastic parts are described by usual wave equations. Therefore, a natural question, which is answered positively, is whether the dissipation localized in the middle part of the bar is sufficient for rendering the whole system exponentially stable. This issue is investigated from the linear operator semigroup point of view, with an emphasis on the case with second sound, namely when Cattaneo’s law for heat conduction is employed. In particular, by means of uniform resolvent bounds for the underlying generator, it is shown that, as time goes to infinity, every solution converges with an exponential rate to a stationary state of the system. Attention is also paid to how and where the choice of heat conduction law as well as the particular material arrangement influence the mathematical analysis. This talk is based on a joint work with Ya-Guang Wang.