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Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation. Under the assumption that the relaxation kernel decays…

Analysis of PDEs · Mathematics 2020-10-06 Vanja Nikolić , Belkacem Said-Houari

In this paper, we consider the Jordan-Moore-Gibson-Thompson equation, a third order in time wave equation describing the nonlinear propagation of sound that avoids the infinite signal speed paradox of classical second order in time strongly…

Analysis of PDEs · Mathematics 2019-10-15 Barbara Kaltenbacher , Vanja Nikolić

We analyze the behavior of third-order in time linear and nonlinear sound waves in thermally relaxing fluids and gases as the sound diffusivity vanishes. The nonlinear acoustic propagation is modeled by the Jordan--Moore--Gibson--Thompson…

Analysis of PDEs · Mathematics 2021-04-13 Barbara Kaltenbacher , Vanja Nikolić

In this paper, we consider the 3D Jordan--Moore--Gibson--Thompson equation arising in nonlinear acoustics. First, we prove that the solution exists globally in time provided that the lower order Sobolev norms of the initial data are…

Analysis of PDEs · Mathematics 2021-04-26 Belkacem Said-Houari

We study the Jordan--Moore--Gibson--Thompson (JMGT) equation, a third order in time wave equation that models nonlinear sound propagation, in the practically relevant setting of Neumann and absorbing boundary conditions. In the analysis, we…

Analysis of PDEs · Mathematics 2019-02-28 Barbara Kaltenbacher , Vanja Nikolić

In nonlinear acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In the literature, these families of equations came to be known as…

Analysis of PDEs · Mathematics 2025-07-03 Mostafa Meliani , Belkacem Said-Houari

Motivated by applications of nonlinear ultrasonics under continuous wave excitation, we study the Jordan-Moore-Gibson-Thompson (JMGT) equation -- a third order in time quasilinear PDE -- under time periodicity conditions. Here the…

Analysis of PDEs · Mathematics 2024-09-10 Barbara Kaltenbacher

This manuscript considers the viscous/inviscid Moore-Gibson-Thompson (MGT) equations with memory of type I in the whole space $\mathbb{R}^n$. For one thing, associating with a new condition on initial data, we derive the optimal $L^2$…

Analysis of PDEs · Mathematics 2024-05-29 Wenhui Chen

In this paper, we consider the inverse problem of recovering a time-dependent nonlinearity for a third order nonlinear acoustic equation, which is known as the Jordan-Moore-Gibson-Thompson equation (J-M-G-T equation for short). This third…

Analysis of PDEs · Mathematics 2023-10-06 Song-Ren Fu , Peng-Fei Yao , Yongyi Yu

The family of Jordan-Moore-Gibson-Thompson (JMGT) equations arises in nonlinear acoustics when a relaxed version of the heat flux law is employed within the system of governing equations of sound motion. Motivated by the propagation of…

Analysis of PDEs · Mathematics 2023-02-14 Barbara Kaltenbacher , Vanja Nikolić

In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan--Moore--Gibson--Thompson equation. This equation arises as an alternative model to the well-known Kuznetsov equation in acoustics. We prove…

Analysis of PDEs · Mathematics 2022-03-10 Belkacem Said-Houari

This paper aims to explore the long-term behavior of some nonlocal high-order-in-time wave equations. These equations, which have come to be known as Moore--Gibson--Thompson equations, arise in the context of acoustic wave propagation when…

Analysis of PDEs · Mathematics 2024-08-09 Mostafa Meliani , Belkacem Said-Houari

When high-frequency sound waves travel through media with anomalous diffusion, such as biological tissues, their motion can be described by nonlinear wave equations of fractional higher order. These can be understood as nonlocal…

Analysis of PDEs · Mathematics 2023-10-31 Vanja Nikolić

We undertake a regularity analysis of the solutions to initial/boundary value problems for the (third-order in time) Moore-Gibson-Thompson (MGT) equation. The key to the present investigation is that the MGT equation falls within a large…

Analysis of PDEs · Mathematics 2018-01-01 Francesca Bucci , Luciano Pandolfi

The Jordan--Moore--Gibson--Thompson (JMGT) equation is a well-established and recently widely studied model for nonlinear acoustics (NLA). It is a third-order (in time) semilinear Partial Differential Equation (PDE) model with the…

Analysis of PDEs · Mathematics 2022-01-03 Marcelo Bongarti , Irena Lasiecka , José Henrique Rodrigues

In this article, we study the Calder\'on problem for nonlocal generalizations of the semilinear Moore--Gibson--Thompson (MGT) equation and the Jordan--Moore--Gibson--Thompson (JMGT) equation of Westervelt-type. These partial differential…

Analysis of PDEs · Mathematics 2026-01-23 Song-Ren Fu , Yongyi Yu , Philipp Zimmermann

In this paper, we consider the Jordan--Moore--Gibson--Thompson with a time-fractional damping term of the type $\delta \textup{D}_t^{1-\alpha} \Delta \psit$ where we allow the challenging so-called critical case ($\delta=0$). This equation…

Analysis of PDEs · Mathematics 2024-10-24 Mostafa Meliani , Belkacem Said-Houari

In this paper, we study the Moore--Gibson--Thompson equation in $\mathbb{R}^N$, which is a third order in time equation that arises in viscous thermally relaxing fluids and also in viscoelastic materials (then under the name of…

Analysis of PDEs · Mathematics 2019-03-26 Marta Pellicer , Belkacem Said-Houari

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…

Analysis of PDEs · Mathematics 2026-04-09 Barbara Kaltenbacher

This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity…

Analysis of PDEs · Mathematics 2025-08-05 Barbara Kaltenbacher
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