DECAY-RATES OF SOLUTIONS OF AN ANISOTROPIC INHOMOGENEOUS N-DIMENSIONAL VISCOELASTIC EQUATION WITH POLYNOMIALLY DECAYING KERNELS

We consider the anisotropic and inhomogeneous viscoelastic equation an d we prove that the first and second order energy decay polynomially a s time goes to infinity when the relaxation function also decays polyn omially to zero. That is, if the kernel G(ijkl) satisfies G(ijkl) less than or equal to -c(0)G(ijkl)(1+1/p); and G(ijkl), G(ijkl)(1+1/p) eps ilon L(1) (IR) for p > 2 such that 2(m)-1 < p, then the first and seco nd order energy decay as 1/(1+t)(q) with q = 2(m)-1.