Relaxation of regularity for the Westervelt equation by nonlinear   damping with application in acoustic-acoustic and elastic-acoustic coupling
  In this paper we show local (and partially global) in time existence for the Westervelt equation with several versions of nonlinear damping. This enables us to prove well-posedness with spatially varying $L_\infty$-coefficients, which includes the situation of interface coupling between linear and nonlinear acoustics as well as between linear elasticity and nonlinear acoustics, as relevant, e.g., in high intensity focused ultrasound (HIFU) applications. 
Rainer Brunnhuber, Barbara Kaltenbacher, Petronela Radu
math.AP