Electron. J. Diff. Equ., Vol. 2012 (2012), No. 48, pp. 1-13.

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

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
email: lucifatori@uel.br
Maria Zegarra Garay
Universidad Nacional Mayor de San Marcos
Facultad de Ciencias, Lima, Peru
email: mzgaray@hotmail.com
Jaime E. Muñnoz Rivera
National Laboratory of Scientific Computations, LNCC/MCT
Institute of Mathematics, UFRJ, RJ, Brazil
email: rivera@lncc.br

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