On the persistence of spatial analyticity for the Beam Equation

Abstract

Persistence of spatial analyticity is studied for solution of the beam equation $u_{tt}+\left(m+{\Delta }^2\right)u+|u{|}^{p-1}u=0$ on ${\mathbb{R}}^n\times \mathbb{R}$. In particular, for a class of analytic initial data with a uniform radius of analyticity ${\sigma }_0$, we obtain an asymptotic lower bound $\sigma (t)\ge c/\sqrt{t}$ on the uniform radius of analyticity $\sigma (t)$ of solution $u(\cdot ,t)$, as $t\to \infty .$

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