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6 papers
Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains
Vanja Nikolić, Belkacem Said-Houari
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…
A high-order discontinuous Galerkin method for nonlinear sound waves
Paola. F. Antonietti, Ilario Mazzieri, Markus Muhr +2
We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on polytopic meshes. To model sound propagation with and without losses, we use Westervelt's nonl…
Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
Marvin Fritz, Ernesto A. B. F. Lima, Vanja Nikolić +2
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volu…
Vanishing relaxation time limit of the Jordan--Moore--Gibson--Thompson wave equation with Neumann and absorbing boundary conditions
Barbara Kaltenbacher, Vanja Nikolić
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 Ne…
On the Jordan-Moore-Gibson-Thompson equation: well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time
Barbara Kaltenbacher, Vanja Nikolić
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 sig…
Isogeometric shape optimization for nonlinear ultrasound focusing
Markus Muhr, Vanja Nikolić, Barbara Wohlmuth +1
The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is…