The talk Some aspects of nonlinear thermoelastic plates, by Michael Pokojovy, will be held on Monday October 5, 2015 at 9:00 in room K3.
In the first part of this talk, we present a solution theory for a nonlinear thermoelastic Reissner-Mindlin plate system with hyperbolic heat conduction in a bounded smooth domain. After having studied the linearized problem and established an exponential stability result under an appropriate frictional damping, we prove a local existence and uniqueness theorem for the nonlinear problem based on classical results for symmetric hyperbolic first-order systems. Based on energy estimates and the barrier method, the local classical solution is then extended to a unique global one provided the initial data are sufficiently small in an appropriate norm. In the second part of our talk, we address a similar problem for a thermoelastic Kirchhoff plate with parabolic heat conduction. With the system being hyperbolic-parabolic, the results on hyperbolic systems are no more directly applicable. Therefore, a Kato-type local solution theory is established. By proving an energy estimate, the barrier method is once again used to obtain a unique global solution. At the end of our talk, we make some comments and give an outlook on our future work.