Some results on the asymptotic behavior for hyperbolic problems in cylindrical domains becoming unbounded

We study here the asymptotic behavior of the solution of a hyperbolic problem defined on a cylindrical domain [0,T] × (− , )p × ω ⊂ [0,T] × Rn when →∞. We show that, under very general assumptions, the solution of this problem converges faster than any power of 1 towards the solution of another hyperbolic problem, defined on [0,T] × ω, in any bounded subdomain. We give both necessary and sufficient conditions for this convergence to occur. © 2007 Elsevier Inc. All rights reserved.