- 4607B South Hall
In this talk, we consider the existence of the global solution and its asymptotic profile for the Cauchy problem for the nonlinear damped beam equation. We show that the equation admits a unique global solution with small slowly decaying data. Moreover we show that the solution can be approximated by the solution of the linear heat equation with suitable data. The proof is based upon the estimates for the evolution operator of the linearized equation in the homogeneous Sobolev space.