We address the energy transfer in the differential system {uttt+αutt−βΔut−γΔu=−ηΔθθt−κΔθ=ηΔutt+αηΔut 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.

Conti, M., Liverani, L., Pata, V. (2021). The MGT-Fourier model in the supercritical case. JOURNAL OF DIFFERENTIAL EQUATIONS, 301, 543-567 [10.1016/j.jde.2021.08.030].

The MGT-Fourier model in the supercritical case

Lorenzo Liverani
Co-primo
;
2021

Abstract

We address the energy transfer in the differential system {uttt+αutt−βΔut−γΔu=−ηΔθθt−κΔθ=ηΔutt+αηΔut 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.
Articolo in rivista - Articolo scientifico
Critical and supercritical regime; Exponential stability; Fourier law; MGT equation; Solution semigroup; Thermoviscoelasticity;
English
2021
301
543
567
reserved
Conti, M., Liverani, L., Pata, V. (2021). The MGT-Fourier model in the supercritical case. JOURNAL OF DIFFERENTIAL EQUATIONS, 301, 543-567 [10.1016/j.jde.2021.08.030].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/414916
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