Jem. Rivera et Ec. Lapa, DECAY-RATES OF SOLUTIONS OF AN ANISOTROPIC INHOMOGENEOUS N-DIMENSIONAL VISCOELASTIC EQUATION WITH POLYNOMIALLY DECAYING KERNELS, Communications in Mathematical Physics, 177(3), 1996, pp. 583-602
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.