On the Jordan-Moore-Gibson-Thompson equation of nonlinear acoustics

TL;DR

This paper provides a systematic overview of the mathematical analysis of the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics, focusing on well-posedness, attenuation, singular limits, and control problems.

Contribution

It offers a comprehensive review of the existing mathematical literature on the JMGT equation, highlighting key results and open questions in the field.

Findings

Analysis of well-posedness for initial value problems.

Investigation of memory and fractional attenuation effects.

Discussion of singular limits and control problems.

Abstract

The JMGT equation was put forward by Pedro Jordan~\cite{jordan2008nonlinear,jordan2014second}, also referring to earlier work by Moore and Gibson~\cite{moore1960propagation}, as well as Thompson~\cite{thompson} to amend the infinite speed of sound paradox of classical models of nonlinear acoustics such as the Westervelt and Kuznetsov's equation. Additionally to its physical significance (and of course related to it), it has given rise to a substantial body of mathematical literature -- possibly even more than the above mentioned classical models. In this paper, we aim to provide a systematic (though inevitably incomplete) overview %and indicate some potential open questions. thereby focusing on well-posedness analysis of initial value and time periodic problems, memory and fractional attenuation as well as singular limits and -- with one example each -- control and inverse problems.