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Uniform Rates of Decay in Anisotropic Thermo-Viscoelasticity

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Abstract

We consider the anisotropic and inhomogeneous thermo-viscoelastic equation. We prove that the first and second-order energy decay exponentially as time goes to infinity provided the relaxation function also decays exponentially to zero. While if the relaxation functions decay polynomially to zero, then the energy decays also polynomially. That is, the kernel of the convolution defines the rate of decay of the solution.

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Authors and Affiliations

  1. Department of Research and Development, National Laboratory for Scientific Computation, Rua Lauro Müller 455, Botafogo Cep. 22290, Rio de Janeiro, RJ, Brasil

    Jaime E. Muñoz Rivera

  2. IM, Federal University of Rio de Janeiro, Brasil

    Jaime E. Muñoz Rivera

  3. Department of Mathematics of, Fluminense University, Rio de Janeiro, Brasil

    Rioco Kamei Barreto

Authors
  1. Jaime E. Muñoz Rivera
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  2. Rioco Kamei Barreto
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Muñoz Rivera, J.E., Barreto, R.K. Uniform Rates of Decay in Anisotropic Thermo-Viscoelasticity. Acta Applicandae Mathematicae 50, 207–224 (1998). https://doi.org/10.1023/A:1005830811242

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  • DOI: https://doi.org/10.1023/A:1005830811242

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