Large time asymptotic behavior for the weakly damped Jordan-Moore-Gibson-Thompson equation

Abstract

This manuscript considers the Jordan-Moore-Gibson-Thompson (JMGT) equation and its linearized equation with an additional weak damping term (proposed by [B. Kaltenbacher, \emph{Inverse Problems} (2025)] firstly) in the whole space $\mathbb{R}^n$. We mainly study the unique existence and large time behavior, including optimal decay estimates and asymptotic profiles, of global in-time Sobolev solutions for any $n\geqslant 1$. This weak damping term leads to diffusion profiles in the sub-critical case $\delta>0$ and regularity-loss decay properties in the critical case $\delta=0$, which are greatly different from the results for the corresponding classical models without the weak damping term.