# Decay rates of solutions of an anisotropic inhomogeneous*n*-dimensional viscoelastic equation with polynomially decaying kernels

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## 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 kernel then the first and second order energy decay as\(\frac{1}{{(1 + t)^q }}\) with

*G*_{ ijkl }satisfies$$\dot G_{ijkl} \leqq - c_0 G_{ijkl}^{1 + \frac{1}{p}} ;and G_{ijkl} ,G_{ijkl}^{1 + \frac{1}{p}} \in L^1 (\mathbb{R})for p > 2such that 2^m - 1< p,$$

*q=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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