# Global solutions to a structure acoustic interaction model with nonlinear sources

## TL;DR

This paper establishes the existence of local and global weak solutions for a coupled structural acoustic interaction model with nonlinear sources, using Galerkin approximation and parameter conditions.

## Contribution

It introduces a rigorous proof of local and global solutions for a strongly coupled nonlinear wave and plate system with arbitrary growth source terms.

## Key findings

- Existence of local weak solutions via Galerkin approximation.
- Conditions for global-in-time solutions.
- Continuous dependence on initial data.

## Abstract

This article focuses on a structural acoustic interaction system consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\R^3$ which is strongly coupled with a Berger plate equation acting only on a flat part of the boundary of $\Omega$. In particular, the source terms acting on the wave and plate equations are allowed to have arbitrary growth order. We employ a standard Galerkin approximation scheme to establish a rigorous proof of the existence of local weak solutions. In addition, under some conditions on the parameters in the system, we prove such solutions exist globally in time and depend continuously on the initial data.