[AN] Chenxi Deng: Stability and Optimal Decay Rates for Abstract Thermoelastic Systems with Cattaneo's law

07 May 2024 16:00 till 17:00 - Location: EEMCS Lecture hall Chip | Add to my calendar

Thermoelastic system describes the interaction between heat conduction and material deformation in solids, which is widely used in materials science, engineering, and physics. In this talk, we will discuss the polynomial stability of abstract thermoelastic systems that follow Cattaneo's type of heat conduction law. Cattaneo's law describes finite heat propagation speed in a medium, which resolves the paradox of infinite speed of heat transfer in Fourier's law. The study encompasses two cases: systems with and without inertial terms. For systems incorporating inertial terms, by analyzing the spectral properties of the system's generator, we partition the parameter space involving coupling, thermal dissipation, and the inertial term into four parts. The polynomial decay rate of each part is proved. Furthermore, the optimality of three of them is also obtained. In the case without inertial terms, we divide the parameter space into three parts and present the optimal polynomial decay rate for each part.