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, issue 1

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 σ(t) 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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https://doi.org/10.1155/ijde/5781898

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnijde:v:2025:y:2025:i:1:n:5781898

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