Article Contents
Article Contents

# 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.
Mathematics Subject Classification: Primary: 93D15; Secondary: 35L70, 35L05, 37L15.

 Citation:

Open Access Under a Creative Commons license