ON THE STABILIZATION OF DYNAMIC ELASTICITY EQUATIONS WITH UNBOUNDED LOCALLY DISTRIBUTED DISSIPATION

摘要

We consider the dynamic elasticity equations with a locally distributed damping in a bounded domain. The local dissipation of the form a(x)yt allows coefficients a that lie in some Lr(Ω), with (r > 2). Using multiplier techniques, interpolation inequalities, and a judicious application of the Holder inequality, we prove sharp energy decay estimates for all r > Max(2,N), where N denotes the space dimension. All space dimensions are considered; the results obtained generalize and improve earlier works where r is required to satisfy r ≥3N+9N2-16N~2(1/2)/4 for N ≥ 3.