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