The MGT-Fourier model in the supercritical case

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:301

Article

Conti, Monica¹  Liverani, Lorenzo¹  Pata, Vittorino¹ 

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

关键词: MGT equation;    Fourier law;    Thermoviscoelasticity;    Critical and supercritical regime;    Solution semigroup;    Exponential stability;   

DOI  :  10.1016/j.jde.2021.08.030

来源: Elsevier

【 摘 要 】

We address the energy transfer in the differential system {u(ttt) +alpha(utt) - beta Delta(ut) - gamma Delta u = -n Delta u = -eta Delta theta theta(t) - kappa Delta theta = eta Delta(utt) + alpha n Delta u(t) made by a Moore-Gibson-Thompson equation in the supercritical regime, hence antidissipative, coupled with the classical heat equation. The asymptotic properties of the related solution semigroup depend on the strength of the coupling, ruling the competition between the Fourier damping and the MGT antidamping. Exponential stability will be shown always to occur, provided that the coupling constant is sufficiently large with respect to the other structural parameters. A fact of general interest will be also discussed, namely, the impossibility of attaining the optimal exponential decay rate of a given dissipative system via energy estimates. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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