Lower bounds of spatial analyticity radius for Benjamin-Bona-Mahony equation on the circle

Document Type : Research Article

Author

Department of Mathematics, Mekdela Amba University, Ethiopia

Abstract

It is shown  that the radius of spatial analyticity $\sigma(t)$ of the  solution $u(t)$ for the Benjamin-Bona-Mahony equation on the circle  does not decay faster than {$c|t|^{-2/3}$} (for some constant $c>0$) as $|t| \to \infty$ . This improves the work [A. A. Himonas, G. Petronilho, Evolution of the radius of spatial analyticity for the periodic Benjamin-Bona-Mahony Equation, Proc. Amer. Math. Soc. 148 (2020) 2953--2967], where the authors obtained a decay rate of order $ct^{-1}$ for large $t$.     The proof of our main theorems is based on a modified Gevrey space, Cauchy-Schwartz inequality, a method of almost conservation law and  Sobolev embedding.

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Journal of Mathematical Modeling
Volume 13, Issue 1
March 2025
Pages 201-208

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