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Boundary Observability and Stabilization for Westervelt Type Wave Equations without Interior Damping

Research paper by Barbara Kaltenbacher

Indexed on: 16 Jun '10Published on: 16 Jun '10Published in: Applied Mathematics & Optimization



Abstract

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.