Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound
We consider an initial–boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell–Cattaneo–Vernotte law giving rise to a ‘second sound’ effect. We study the local well-posedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev Hk-spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small – not in the full topology of our solution class, but in a lower topology corresponding to weak solutions we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.
Nonlinear Analysis, Theory, Methods and Applications
Lasiecka, I., Pokojovy, M., & Wan, X. (2019). Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound. Nonlinear Analysis, Theory, Methods and Applications, 186, 219-258. https://doi.org/10.1016/j.na.2019.02.019