Asymptotic Behavior of Solutions for the Wave Equation
 With  Damping Concentrated in interior curves
                          by
                  Marius Tucsnak,
 Ecole Polytechnique,  Centre de Mathematiques appliquees, 
91128 Palaiseau Cedex and Universite de Versailles
                        and
                  Enrique Zuazua,
     Departamento de Matematica Aplicada, 
     Universidad Complutense, 28040 Madrid




We consider an initial and boundary value problem 
 for the two dimensional wave equation  with nonlinear
 damping concentrated on an interior 
 curve. By the use of the theory of nonlinear semigroups we prove a 
 wellposedness result. The main result asserts 
 that generically (i.e. for almost all interior curves) 
 the solutions decay to zero in the energy space. We also show,
 that whatever the interior curve is, the decay is not uniform.
 

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