Well-posedness of a Nonlinear Acoustics -- Structure Interaction Model

TL;DR

This paper proves the well-posedness of a coupled nonlinear acoustic-structure interaction model involving the Westervelt equation and a lower-dimensional interface, introducing a new variational formulation and analyzing boundary conditions.

Contribution

It establishes well-posedness for a novel coupled nonlinear acoustic-structure model, filling a gap in the literature and proposing a new variational weak formulation.

Findings

Proved local and global well-posedness for small data.

Developed a novel variational weak formulation.

Analyzed effects of various boundary conditions.

Abstract

We establish local-in-time and global in time well-posedness for small data, for a coupled system of nonlinear acoustic structure interactions. The model consists of the nonlinear Westervelt equation on a bounded domain with non homogeneous boundary conditions, coupled with a 4th order linear equation defined on a lower dimensional interface occupying part of the boundary of the domain, with transmission boundary conditions matching acoustic velocities and acoustic pressures. While the well-posedness of the Westervelt model has been well studied in the literature, there has been no works on the literature on the coupled structure acoustic interaction model involving the Westervelt equation. Another contribution of this work, is a novel variational weak formulation of the linearized system and a consideration of various boundary conditions.