We study the long-term behaviour of solutions to a one-dimensional coupled wave- heat system with Coleman–Gurtin thermal law. Our approach is based on the asymptotic theory of C0-semigroups and recent results developed for coupled control systems. As our main results, we represent the system as a feedback interconnection between the wave part and the Coleman–Gurtin part and we show that the associated semigroup in the history framework of Dafermos is polynomially stable with optimal decay rate t^(−2) as t → ∞. In particular, we obtain a sharp estimate for the rate of energy decay of classical solutions to the problem.
Optimal decay for a wave-heat system with Coleman-Gurtin thermal law
Filippo Dell'Oro;
2023-01-01
Abstract
We study the long-term behaviour of solutions to a one-dimensional coupled wave- heat system with Coleman–Gurtin thermal law. Our approach is based on the asymptotic theory of C0-semigroups and recent results developed for coupled control systems. As our main results, we represent the system as a feedback interconnection between the wave part and the Coleman–Gurtin part and we show that the associated semigroup in the history framework of Dafermos is polynomially stable with optimal decay rate t^(−2) as t → ∞. In particular, we obtain a sharp estimate for the rate of energy decay of classical solutions to the problem.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
