Spatial energy decay estimate in dynamical problems for a micropolar viscoelastic solid

This paper concerns some estimes of the energy for a micropolar viscoelastic solid in dynamical problems. First, under the assumptions that the solid occupies a semi-infinite cylinder and that the boundary values vanish only on the base, we estimate for any fixed t > 0, in terms of initial and boundary data, the energy of the portions of the solid at distance greater than z from the base and its norm in L^1(0, t). Finally these results are extended to more general domains under the hypothesis that the initial and boundary data have a bounded support. In our analysis we make use of a Maximal Free Energy which allows us to impose very mild restrictions on the relaxation functions.