Local well-posedness of a coupled Westervelt-Pennes model of nonlinear ultrasonic heating

Abstract

High-Intensity Focused Ultrasound (HIFU) waves are known to induce localized heat to a targeted area during medical treatments. In turn, the rise in temperature influences their speed of propagation. This coupling affects the position of the focal region as well as the achieved pressure and temperature values. In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Westervelt wave equation coupled to the Pennes bioheat equation that captures this so-called thermal lensing effect. We prove that this quasi-linear model is well-posed locally in time and does not degenerate under a smallness assumption on the pressure data.

References in corpus (2)

• Optimal regularity and long-time behavior of solutions for the Westervelt equation
• Parabolic approximation of quasilinear wave equations with applications in nonlinear acoustics