On the persistence of spatial analyticity for the Beam Equation

Persistence of spatial analyticity is studied for solution of the beam equation $u_{tt} + \left(m+Δ^2\right) u + |u|^{p-1}u = 0$ on $\mathbb R^n \times \mathbb R$. In particular, for a class of analytic initial data with a uniform radius of analyticity $σ_0$, we obtain an asymptotic lower bound $σ(t) \ge c/\sqrt t$ on the uniform radius of analyticity $σ(t)$ of solution $u(\cdot, t)$, as $t \rightarrow \infty.$

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