EXISTENCE AND UNIFORM DECAY FOR A NONLINEAR BEAM EQUATION WITH NONLINEARITY OF KIRCHHOFF TYPE IN DOMAINS WITH MOVING BOUNDARY

摘要

We prove the exponential decay in the case n > 2, as time goes to infinity, of regular so-lutions for the nonlinear beam equation with memory and weak damping utt +Δ2u—M(||▽u||2L2(Ωt)Δu + ∫tog(t - s)Δu(s)ds + αut = OinQΛ in a noncylindrical domain of Rn+ (n ≥ 1) under suitable hypothesis on the scalar functions M and g, and where a is a positive constant. We establish existence and uniqueness of regular solutions for any n≥1.