A nonlinear multiphysics model motivated by ultrasound-enhanced drug delivery in cancer treatment is presented. The acoustic pressure field is modeled by Westervelt's quasilinear wave equation including temperature-dependent coefficient functions and a nonlocal attenuation acoustic damping of time-fractional type. The wave equation is strongly coupled to the nonlinear Pennes heat equation with a pressure-dependent source to account for ultrasound waves heating up the tissue. The drug concentration is modeled by a advection-diffusion equation with convective velocity depending on the acoustic pressure, its gradient and temperature. The well-posedness analysis of the coupled system is developed by means of a fixed-point iteration argument combined with devising energy estimates that can accommodate the time-fractional damping. The energy arguments are, in part, carried out by employing time-weighted test functions to reduce the regularity assumptions on the initial temperature. Our theoretical considerations are complemented by a numerical investigation of the system under more realistic boundary conditions. The numerical experiments, performed in different computational scenarios, underline the importance of considering nonlinear effects when modeling ultrasound-targeted drug delivery.
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