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

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  • Tegegne Getachew

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.

Suggested Citation

  • Tegegne Getachew, 2025. "Asymptotic Lower Bound on the Spatial Analyticity Radius for Solutions of the Periodic Fifth Order KdV–BBM Equation," International Journal of Differential Equations, Hindawi, vol. 2025, pages 1-9, April.
    • Handle: RePEc:hin:jnijde:5781898
    DOI: 10.1155/ijde/5781898
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