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Applied Mathematics & Optimization

, Volume 62, Issue 3, pp 381–410 | Cite as

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

  • Barbara Kaltenbacher
Article

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.

Keywords

Nonlinear wave equation Westervelt equation Hyperbolic equations Boundary feedback control Absorbing boundary conditions Stabilization 

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University of GrazGrazAustria

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