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. © 2012 Texas State University - San Marcos.
|Original language||American English|
|Number of pages||13|
|Journal||Electronic Journal of Differential Equations|
|State||Published - 10 Apr 2012|