The Westervelt–Pennes model of nonlinear thermoacoustics: Global solvability and asymptotic behavior

Abstract

In this work, we investigate the global well-posedness and asymptotic behavior of a mathematical model of ultrasound-induced heating based on a coupled system of Westervelt's nonlinear acoustic wave equation and Pennes bioheat equation. To this end, under Dirichlet–Dirichlet boundary conditions, we prove global existence for sufficiently small and smooth solutions of the nonlinear model using an energy method. In addition, we show that the energy norm of the resulting pressure and temperature decays to the steady state exponentially fast.