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Stabilization of mixture of two rigid solids modeling temperature and porosity
(Applied Mathematics Letters, 2012-05) Alves, Margareth S.; Rivera, Jaime E. Muñoz; Sepúlveda, Mauricio; Villagrán, Octavio P. Vera
In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.
Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture
(Acta Mechanica, 2011-06) Alves, Margareth S.; Rivera, Jaime E. Muñoz; Sepúlveda, Mauricio; Vera, Octavio
In this paper, we investigate the asymptotic behavior of solutions to the initial boundary value problem for the interaction between the temperature field and the porosity fields in a homogeneous and isotropic mixture from the linear theory of porous Kelvin–Voigt materials. Our main result is to establish conditions which insure the analyticity and the exponential stability of the corresponding semigroup. We show that under certain conditions for the coefficients we obtain a lack of exponential stability. A numerical scheme is given.