On the persistence of spatial analyticity for the beam equation

Abstract

Persistence of spatial analyticity is studied for solution of the beam equation utt+(m+Δ2)u+|u|p−1u=0 on Rn×R. In particular, for a class of analytic initial data with a uniform radius of analyticity σ0, we obtain an asymptotic lower bound σ(t)⩾c/t on the uniform radius of analyticity σ(t) of solution u(⋅,t), as t→∞.