Exponential stability of a thermoelastic system without mechanical dissipation
We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in , as was that of the analytic case-where rotational forces are neglected-in ); both the analytic and nonanalytic cases are treated here. The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for such work. Moreover, the particular choice of multiplier becomes clear only after recasting the pde model into an associated abstract Evolution Equation. With this direct technique, we also obtain an exponential stability estimate pertaining to the limit case in which rotational inertia is neglected, and which leads to an associated analytic semigroup.
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
28 (1996) s.
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
George Avalos, Irena Lasiecka, "Exponential stability of a thermoelastic system without mechanical dissipation", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 28 (1996) suppl., pp. 1-28.