ON THE MOORE-GIBSON-THOMPSON EQUATION WITH THERMAL EFFECTS OF GURTIN-PIPKIN TYPE

被引：3

作者：

Dell'oro, Filippo ^{[1
]}

Pata, Vittorino ^{[1
]}

机构：

[1] Politecn Milan, I-20133 Milan, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 12期

关键词：

MGT equation; Gurtin-Pipkin equation; solution semigroup; lack of exponential stability; LINEAR SOLID MODEL; TIMOSHENKO SYSTEMS; VISCOELASTIC PLATE; SPECTRAL-ANALYSIS; HEAT-CONDUCTION; STABILITY; PROPAGATION; ANALYTICITY; SEMIGROUPS; VIBRATIONS;

D O I：

10.3934/dcdss.2023051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Moore-Gibson-Thompson-Gurtin-Pipkin model {u(ttt) + alpha u(tt) - beta Delta u(t) - gamma Delta u = rho Delta theta theta(t) - integral(infinity)(0) g(s)Delta theta(t - s)ds = rho Delta u(tt) + rho alpha Delta u(t) with the first equation in the subcritical regime alpha beta > gamma. The system generates a strongly continuous semigroup of linear contractions which is never exponentially stable, even if the second equation, when uncoupled, generates an exponentially stable semigroup. This is in deep contrast to what happens in connection with the semigroup generated by the Moore-Gibson-Thompson Fourier system {u(ttt) + alpha u(tt) - beta Delta u(t) - gamma Delta u = rho Delta theta theta(t) - nu Delta theta = rho Delta u(tt) + rho alpha Delta u(t) formally obtained as a limit by letting g -> nu delta(0+).

引用

页码：3459 / 3472

页数：14

共 38 条

[1] Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect [J].