Mathematical Models and Methods in Applied Sciences ( IF 3.5 ) Pub Date : 2022-04-30 , DOI: 10.1142/s0218202522500221 Barbara Kaltenbacher 1 , Vanja Nikolić 2
In this paper, we consider several time-fractional generalizations of the Jordan–Moore–Gibson–Thompson (JMGT) equations in nonlinear acoustics as well as their linear Moore–Gibson–Thompson (MGT) versions. Following the procedure described in Jordan (2014), these time-fractional acoustic equations are derived from four fractional versions of the Maxwell–Cattaneo law in Compte and Metzler (1997). Additionally to providing well-posedness results for each of them, we also study the respective limits as the fractional order tends to one, leading to the classical third order in time (J)MGT equation.
中文翻译:
时间分数摩尔-吉布森-汤普森方程
在本文中,我们考虑了非线性声学中 Jordan-Moore-Gibson-Thompson (JMGT) 方程及其线性 Moore-Gibson-Thompson (MGT) 方程的几种时间分数推广。按照 Jordan (2014) 中描述的程序,这些时间分数声学方程是从 Compte 和 Metzler (1997) 中的 Maxwell-Cattaneo 定律的四个分数版本推导出来的。除了为它们中的每一个提供适定性结果外,我们还研究了分数阶趋于一时的各自极限,从而得出经典的时间三阶 (J)MGT 方程。