Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 48, pp. 1-13.

Title: Differentiability, analyticity and optimal rates of decay for
       damped wave equations

Authors: Luci Harue Fatori (Univ. Estadual de Londrina, PR, Brazil)
         Maria Zegarra Garay (Univ. Nacional Mayor de San Marcos, Lima, Peru)
	 Jaime E. Munoz Rivera  (Univ. Federal do Rio de Janeiro, Brazil)

Abstract:
 We give necessary and sufficient conditions on the damping term of a wave 
 equation for the corresponding  semigroup to be analytic. We characterize 
 damped  operators for which the corresponding semigroup is analytic, 
 differentiable, or exponentially stable. 
 Also when the damping operator is not strong enough to have the above 
 properties, we show that the solution decays  polynomially, and that 
 the polynomial rate of decay is optimal.
 
Submitted December 22, 2011. Published March 27, 2012.
Math Subject Classifications: 35L10, 47D06.
Key Words: Dissipative systems; decay rate; analytic semigroups; 
           polynomial stability.