# Long-time behavior of quasilinear thermoelastic Kirchhoff-Love plates with second sound

Lasiecka, Irena; Pokojovy, Michael; Wan, Xiang

##### Abstract:
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 $\textit{H}$$^{k}$-spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small in a lower topology (basic energy level corresponding to weak solutions), we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht/Preprint Publikationsjahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X urn:nbn:de:swb:90-873139 KITopen-ID: 1000087313 Verlag KIT, Karlsruhe Umfang 46 S. Serie CRC 1173 ; 2018/31 Schlagwörter Kirchhoff-Love plates, nonlinear thermoelasticity, hyperbolic thermoelasticity, global well-posedness, classical solutions, exponential stability
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page