Lower bound on the radius of analyticity of solution for fifth order KdV-BBM Equation

Abstract

We show that the uniform radius of spatial analyticity $\sigma(t)$ of solution at time $t$ for the fifth order KdV-BBM equation cannot decay faster than $1/t$ for large $t>0$, given initial data that is analytic with fixed radius $\sigma_0$. This significantly improves a recent result by Carvajal and Panthee, where they established an exponential decay of $\sigma(t)$ for large $t$.