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2009, 2009(Special): 744-752. doi: 10.3934/proc.2009.2009.744

Equivalence between observability and stabilization for a class of second order semilinear evolution

Louis Tcheugoue Tebou 1,

1. 

Department of Mathematics, Florida International University, University Park, Miami, Florida 33199, United States

Received  August 2008 Revised  February 2009 Published  September 2009

We consider an abstract second order semilinear evolution equation with a bounded dissipation. We establish an equivalence between the stabilization of this system and the observability of the corresponding undamped system. Our technique of proof relies on an appropriate decomposition of the solution, and the energy method. Our result generalizes an earlier one by Haraux [5] who studied the same type of problem for linear systems. Some applications of our result are provided, and the paper ends with a few open problems.
Keywords: localized damping, stabilization, observability, hyperbolic equation, elasticity equations, bounded dissipation, semilinear equation, second order evolution equation, Euler-Bernoulli equation.
Mathematics Subject Classification: Primary: 93D15; Secondary: 35L70, 35L05, 37L15.
Citation: Louis Tcheugoue Tebou. Equivalence between observability and stabilization for a class of second order semilinear evolution. Conference Publications, 2009, 2009 (Special) : 744-752. doi: 10.3934/proc.2009.2009.744
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