Related papers: On the Jordan-Moore-Gibson-Thompson equation of no…

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…

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…

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…

In this paper, we study large-time behaviors for a fundamental model in nonlinear acoustics, precisely, the viscous Jordan-Moore-Gibson-Thompson (JMGT) equation in the whole space $\mathbb{R}^n$. This model describes nonlinear acoustics in…

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…

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…

The (third-order in time) JMGT equation \cite{Jordan2,HCP} is a nonlinear (quasi-linear) Partial Differential Equation (PDE) model introduced to describe a nonlinear propagation of sound in an acoustic medium. The important feature is that…

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…

In this paper we prove uniqueness and stability of reconstruction of two coefficients (sound speed and nonlinearity parameter) in the Jordan-Moore-Gibson-Thompson JMGT equation of nonlinear acoustics, relying on observations resulting from…

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…

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…

We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary…

Boundary feedback stabilization of a critical, nonlinear Jordan--Moore--Gibson--Thompson (JMGT) equation is considered. JMGT arises in modeling of acoustic waves involved in medical/engineering treatments like lithotripsy, thermotherapy,…

The Jordan-Moore-Gibson-Thompson (JMGT)\cite{christov_heat_2005,jordan_nonlinear_2008,straughan_heat_2014} equation is a benchmark model describing propagation of nonlinear acoustic waves in heterogeneous fluids at rest. This is a…

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…

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…

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…

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…

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…

In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…