Jameson Graber, University of Virginia


Uniform Stability of a Wave Equation with Porous Acoustic Boundary Condition

Abstract: We consider a structural acoustic wave equation with porous acoustic boundary conditions. This is a coupled system of partial differential equations modeling a hydrodynamic flow in a channel or acoustic pressure in a chamber surrounded by two walls, where one of the walls exhibits some porosity. The latter has a stabilizing effect on the structure. We prove both strong and uniform stability of solutions with initial data in the finite energy space, where the latter is obtained using certain geometric restrictions on the boundary. This result is used to establish global existence and exponential decay of solutions of a nonlinear perturbed system when the solutions have small initial data.

Advisor: Dr. Irena Lasiecka (University of Virginia).