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Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Viçosa-UFV, Viçosa, MG, 36570-000, Brasil

    Margareth S. Alves

  2. Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Petrópolis, RJ, 25651-075, Brasil

    Jaime E. Muñoz Rivera

  3. CI2MA and Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile

    Mauricio Sepúlveda

  4. Departamento de Matemática, Universidad del Bío-Bío, Collao 1202. Casilla 5-C, Concepción, Chile

    Octavio Vera

Authors
  1. Margareth S. Alves
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  2. Jaime E. Muñoz Rivera
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  3. Mauricio Sepúlveda
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  4. Octavio Vera
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Correspondence to Octavio Vera.

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Alves, M.S., Rivera, J.E.M., Sepúlveda, M. et al. Stabilization of a system modeling temperature and porosity fields in a Kelvin–Voigt-type mixture. Acta Mech 219, 145–167 (2011). https://doi.org/10.1007/s00707-010-0443-1

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  • DOI: https://doi.org/10.1007/s00707-010-0443-1

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