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 (On the radius of analyticity for the solution of the fifth order KdV–BBM model, 2020. arXiv:2009.09328) , where they established an exponential decay of \(\sigma (t)\) for large t.