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Communications in Mathematical Physics

, Volume 177, Issue 3, pp 583–602 | Cite as

Decay rates of solutions of an anisotropic inhomogeneousn-dimensional viscoelastic equation with polynomially decaying kernels

  • Jaime E. Muñoz Rivera
  • Eugenio Cabanillas Lapa
Article

Abstract

We consider the anisotropic and inhomogeneous viscoelastic equation and we prove that the first and second order energy decay polynomially as time goes to infinity when the relaxation function also decays polynomially to zero. That is, if the kernelG ijkl satisfies
$$\dot G_{ijkl} \leqq - c_0 G_{ijkl}^{1 + \frac{1}{p}} ;and G_{ijkl} ,G_{ijkl}^{1 + \frac{1}{p}} \in L^1 (\mathbb{R})for p > 2such that 2^m - 1< p,$$
then the first and second order energy decay as\(\frac{1}{{(1 + t)^q }}\) withq=2 m −1.

Keywords

Neural Network Statistical Physic Complex System Decay Rate Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Jaime E. Muñoz Rivera
    • 1
    • 2
  • Eugenio Cabanillas Lapa
    • 3
  1. 1.Department of Research and DevelopmentNational Laboratory for Scientific ComputationRio de JaneiroBrasil
  2. 2.IM, Federal University of Rio de JaneiroRio de JaneiroBrasil
  3. 3.Universidad Nacional Mayor de San MarcosLimaPeru

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