On the Moore-Gibson-Thompson Equation and Its Relation to Linear Viscoelasticity

被引：103

作者：

Dell'Oro, Filippo ^{[1
]}

Pata, Vittorino ^{[1
]}

机构：

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

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2017年 / 76卷 / 03期

关键词：

Moore-Gibson-Thompson equation; Exponential decay; Linear viscoelasticity; EXPONENTIAL STABILITY; ASYMPTOTIC STABILITY; MEMORY;

D O I：

10.1007/s00245-016-9365-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the parallel between the third-order Moore-Gibson-Thompson equation partial derivative(ttt)u + alpha partial derivative(tt)u - beta Delta partial derivative(tu) - gamma Delta u = 0 depending on the parameters alpha, beta, gamma > 0, and the equation of linear viscoelasticity partial derivative(tt)u(t) - kappa(0)Delta u(t) - integral(infinity)(0) kappa '(s)Delta u(t-s) ds = 0 for the particular choice of the exponential kernel kappa(s) = ae(-bs) + c with a, b, c > 0. In particular, the latter model is shown to exhibit a preservation of regularity for a certain class of initial data, which is unexpected in presence of a general memory kernel kappa.

引用

页码：641 / 655

页数：15

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