We study the regularized MGT equationuttt + alpha utt + beta Aut + gamma Au + delta Autt = 0where A is a strictly positive unbounded operator and alpha, beta, gamma, delta > 0. The effect of the regularizing term delta Autt translates into having an analytic semigroup S(t) = etA of solutions. Moreover, the asymptotic properties of the semigroup are ruled by the stability number Kappa = beta - gamma alpha + delta lambda 0which, contrary to the case of the standard MGT equation, depends also on the minimum lambda 0 > 0 of the spectrum of A.
Dell'Oro, F., Liverani, L., Pata, V. (2023). On the regularized Moore-Gibson-Thompson equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 16(9), 2326-2338 [10.3934/dcdss.2023025].
On the regularized Moore-Gibson-Thompson equation
Liverani, LCo-primo
;
2023
Abstract
We study the regularized MGT equationuttt + alpha utt + beta Aut + gamma Au + delta Autt = 0where A is a strictly positive unbounded operator and alpha, beta, gamma, delta > 0. The effect of the regularizing term delta Autt translates into having an analytic semigroup S(t) = etA of solutions. Moreover, the asymptotic properties of the semigroup are ruled by the stability number Kappa = beta - gamma alpha + delta lambda 0which, contrary to the case of the standard MGT equation, depends also on the minimum lambda 0 > 0 of the spectrum of A.
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