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

TL;DR

This paper establishes local and partial global existence results for the Westervelt equation with nonlinear damping, enabling well-posedness in complex acoustic and elastic coupling scenarios relevant to high intensity focused ultrasound.

Contribution

It introduces new existence results for the Westervelt equation with nonlinear damping, accommodating spatially varying coefficients and interface coupling in acoustics and elasticity.

Findings

Proves local and partial global existence for the Westervelt equation with nonlinear damping.

Enables well-posedness in heterogeneous media with interface coupling.

Applicable to high intensity focused ultrasound (HIFU) scenarios.

Abstract

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.