Luci Harue Fatori, Maria Zegarra Garay, Jaime E. Munoz Rivera
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.
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| Luci Harue Fatori |
Department of Mathematics
Universidade Estadual de Londrina, PR, Brazil
| Maria Zegarra Garay |
Universidad Nacional Mayor de San Marcos
Facultad de Ciencias, Lima, Peru
| Jaime E. Muñnoz Rivera |
National Laboratory of Scientific Computations, LNCC/MCT
Institute of Mathematics, UFRJ, RJ, Brazil
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