Luci Harue Fatori, Maria Zegarra Garay, Jaime E. Munoz Rivera
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.
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Luci Harue Fatori Department of Mathematics Universidade Estadual de Londrina, PR, Brazil email: lucifatori@uel.br |
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Maria Zegarra Garay Universidad Nacional Mayor de San Marcos Facultad de Ciencias, Lima, Peru email: mzgaray@hotmail.com |
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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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