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Lower bounds of spatial analyticity radius for Benjamin-Bona-Mahony equation on the circle | ||
| Journal of Mathematical Modeling | ||
| مقاله 25، دوره 13، شماره 1، خرداد 2025، صفحه 201-208 اصل مقاله (161.44 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.28211.2490 | ||
| نویسنده | ||
| Tegegne Getachew* | ||
| Department of Mathematics, Mekdela Amba University, Ethiopia | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Periodic BBMy Equation؛ Radius of analyticity of solutions؛ Modified Gevrey spaces؛ Lower bound for the radius | ||
| مراجع | ||
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