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On the Jordan-Moore-Gibson-Thompson equation of nonlinear acoustics
Barbara Kaltenbacher
The JMGT equation was put forward by Pedro Jordan~\cite{jordan2008nonlinear,jordan2014second}, also referring to earlier work by Moore and Gibson~\cite{moore1960propagation}, as we…
Imaging nonlinearity coefficient and sound speed with the JMGT equation in frequency domain
Barbara Kaltenbacher
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…
On uniqueness of coefficient identification in the Bloch-Torrey equation for magnetic resonance imaging
Barbara Kaltenbacher
In this paper we provide some uniqueness results for the (multi-)coefficient identification problem of reconstructing the spatially varying spin density as well as the spin-lattice…
Forward and Inverse Problems in Nonlinear Acoustics
Barbara Kaltenbacher
The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harm…
Acoustic nonlinearity parameter tomography with the Jordan-Moore-Gibson-Thompson equation in frequency domain
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 f…
Well-posedness of the time-periodic Jordan-Moore-Gibson-Thompson equation
Barbara Kaltenbacher
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…
Existence, uniqueness, and numerical solutions of the nonlinear periodic Westervelt equation
Benjamin Rainer, Barbara Kaltenbacher
In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in , where , subject to Robin bound…
Existence of solutions to k-Wave models of nonlinear ultrasound propagation in biological tissue
Ben Cox, Barbara Kaltenbacher, Vanja Nikolić +1
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solve…
A first order in time wave equation modeling nonlinear acoustics
Barbara Kaltenbacher, Pascal Lehner
In this paper we focus on a small amplitude approximation of a Navier-Stokes-Fourier system modeling nonlinear acoustics. Omitting all third and higher order terms with respect to…
The Kuznetsov and Blackstock equations of nonlinear acoustics with nonlocal-in-time dissipation
B. Kaltenbacher, M. Meliani, V. Nikolić
In ultrasonics, nonlocal quasilinear wave equations arise when taking into account a class of heat flux laws of Gurtin--Pipkin type within the system of governing equations of soun…