On the Moore-Gibson-Thompson Equation and Its Relation to Linear Viscoelasticity
On the Moore-Gibson-Thompson Equation and Its Relation to Linear Viscoelasticity
复制标题
DOI：
10.1007/s00245-016-9365-1
复制
发表时间：
2017-12-01
影响因子：
1.8
通讯作者：
Pata, Vittorino
中科院分区：
文献类型：
--
作者：
Dell'Oro, Filippo;Pata, Vittorino
本文讨论了三阶Moore-Gibson-Thompson方程u + α偏导数u -β Delta偏导数u-γ Delta u = 0依赖于参数α，β，γ> 0的平行性，线性粘弹性偏导数（tt）u（t）- kappa（0）Δ u（t）-积分方程（无穷大）（0）kappa '（s）Δ u（t-s）ds = 0对于指数核kappa（s）= ae（-bs）+c的特定选择，其中a，B，c > 0。特别是，后者的模型显示出一定的初始数据，这是意想不到的一般内存内核Kappa存在的规则性的保存。
We discuss the parallel between the third-order Moore-Gibson-Thompson equationpartial 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 viscoelasticitypartial derivative(tt)u(t) - kappa(0)Delta u(t) - integral(infinity)(0) kappa '(s)Delta u(t-s) ds = 0for the particular choice of the exponential kernelkappa(s) = ae(-bs) + cwith 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.