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

Lasiecka, Irena; Pokojovy, Michael; Wan, Xiang


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.

Volltext §
DOI: 10.5445/IR/1000087313
Veröffentlicht am 08.11.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000087313
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 46 S.
Serie CRC 1173 ; 2018/31
Schlagwörter Kirchhoff-Love plates, nonlinear thermoelasticity, hyperbolic thermoelasticity, global well-posedness, classical solutions, exponential stability
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