Asymptotic Lower Bound on the Spatial Analyticity Radius for Solutions of the Periodic Fifth Order KdV–BBM Equation

Tegegne Getachew

International Journal of Differential Equations, 2025, vol. 2025, 1-9

Abstract: In this work, consideration is given to the initial value problem associated with the periodic fifth-order KdV–BBM equation. It is shown that the uniform radius of spatial analyticity σt of solution at time t is bounded from below by ct−2/3 (for some c>0), given initial data η0 that is analytic on the circle and has a uniform radius of spatial analyticity σ0. The proof of our main theorems is based on a contraction mapping argument, a method of approximate conservation law in a modified Gevrey spaces, Hölder’s inequality, Sobolev algebra, Cauchy–Schwartz inequality, and Sobolev embedding.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:5781898

DOI: 10.1155/ijde/5781898

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