Relaxation of regularity for the Westervelt equation by nonlinear damping with application in acoustic-acoustic and elastic-acoustic coupling

摘要

In this paper we show local (and partially global) in time existence for theWestervelt equation with several versions of nonlinear damping. This enables usto prove well-posedness with spatially varying $L_\infty$-coefficients, whichincludes the situation of interface coupling between linear and nonlinearacoustics as well as between linear elasticity and nonlinear acoustics, asrelevant, e.g., in high intensity focused ultrasound (HIFU) applications.