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math.AP2024

Mathematical models for nonlinear ultrasound contrast imaging with microbubbles

Vanja Nikolić, Teresa Rauscher

Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of bloo…

math.AP2024

blow-up in the Jordan-Moore-Gibson-Thompson equation

Vanja Nikolić, Michael Winkler

The Jordan-Moore-Gibson-Thompson equation \[ τu_{ttt} + αu_{tt} = βΔu_t + γΔu + (f(u))_{tt} \] is considered in a smoothly bounded domain with $n\leq…

math.AP2024

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…