Acta Mech 219, 145–167 (2011) DOI 10.1007/s00707-010-0443-1 Margareth S. Alves · Jaime E. Muñoz Rivera · Mauricio Sepúlveda · Octavio Vera Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture Received: 14 April 2010 / Published online: 30 January 2011 © Springer-Verlag 2011 Abstract In this paper, we investigate the asymptotic behavior of solutions to the initial boundary value prob- lem 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. 1 Introduction This article is concerned with a special case of a linear theory for the interaction between the temperature field and the porosity fields in a homogeneous and isotropic mixture from the linear theory of porous Kel- vin–Voigt materials. The theory of porous mixtures has been investigated by several authors (see, for instance, [6–8, 10] and the references therein). Iesan and Quintanilla [7] considered binary mixtures where the individual components are modeled as porous Kelvin–Voigt materials, and the volume fraction of each constituent was considered as an independent kinematical quantity. The authors assumed that the constituents have a common temperature and that every thermodynamical process that takes place in the mixture satisfies the Clausius–Du- hem inequality. At the end, they presented as an application the interaction between the temperature field θ and the porosity fields u and w in a homogeneous and isotropic mixture. We restrict ourselves to the interaction between the temperature field and the porosity fields u and w in a homogeneous and isotropic mixture. Under the same assumptions of Ie¸ san and Quintanilla [7], we have a system of three equations given by: M. S. Alves Departamento de Matemática, Universidade Federal de Viçosa-UFV, Viçosa, MG 36570-000, Brasil E-mail: malves@ufv.br J. E. M. Rivera Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Petrópolis, RJ 25651-075, Brasil E-mail: rivera@lncc.br M. Sepúlveda CI 2 MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile E-mail: mauricio@ing-mat.udec.cl O. Vera (B ) Departamento de Matemática, Universidad del Bío-Bío, Collao 1202. Casilla 5-C, Concepción, Chile E-mail: overa@ubiobio.cl