Time-fractional Moore-Gibson-Thompson equations
Analysis of PDEs
2022-03-29 v3
Abstract
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.
Cite
@article{arxiv.2104.13967,
title = {Time-fractional Moore-Gibson-Thompson equations},
author = {Barbara Kaltenbacher and Vanja Nikolić},
journal= {arXiv preprint arXiv:2104.13967},
year = {2022}
}