Neumann-boundary stabilization of the wave equation with damping control and applications

Boumediène Chentouf, Aissa Guesmia

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This article is devoted to the boundary stabilization of a non-homogeneous ndimensional wave equation subject to static or dynamic Neumann boundary conditions. Using a linear feedback law involving only a damping term, we provide a simple method and obtain an asymptotic convergence result for the solutions of the considered systems. The method consists in proposing a new energy norm. Then, a similar result is derived for the case of dynamic Neumann boundary conditions with nonlinear damping feedback laws. Finally, the method presented in this work is also applied to several distributed parameter systems such as the Petrovsky system, coupled wave-wave equations and elasticity systems.

Original languageEnglish
Pages (from-to)541-566
Number of pages26
JournalCommunications in Applied Analysis
Volume14
Issue number3-4
Publication statusPublished - Jul 2010

Fingerprint

Boundary Stabilization
Wave equations
Dynamic Boundary Conditions
Wave equation
Damping
Feedback Law
Stabilization
Boundary conditions
Neumann Boundary Conditions
Feedback
Elasticity
Nonlinear Damping
Damping Term
Asymptotic Convergence
Distributed Parameter Systems
Convergence Results
Coupled System
Norm
Energy

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Modelling and Simulation
  • Numerical Analysis

Cite this

Neumann-boundary stabilization of the wave equation with damping control and applications. / Chentouf, Boumediène; Guesmia, Aissa.

In: Communications in Applied Analysis, Vol. 14, No. 3-4, 07.2010, p. 541-566.

Research output: Contribution to journalArticle

Chentouf, Boumediène ; Guesmia, Aissa. / Neumann-boundary stabilization of the wave equation with damping control and applications. In: Communications in Applied Analysis. 2010 ; Vol. 14, No. 3-4. pp. 541-566.
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