Applied Mathematics and Optimization, Vol.62, No.3, 381-410, 2010
Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping
In this paper we show boundary observability and boundary stabilizability by linear feedbacks for a class of nonlinear wave equations including the undamped Westervelt model used in nonlinear acoustics. We prove local existence for undamped generalized Westervelt equations with homogeneous Dirichlet boundary conditions as well as global existence and exponential decay with absorbing type boundary conditions.
Keywords:Nonlinear wave equation;Westervelt equation;Hyperbolic equations;Boundary feedback control;Absorbing boundary conditions;Stabilization