收稿日期: 2020-05-08
网络出版日期: 2020-09-14
基金资助
国家自然科学基金资助项目(11926319);山西省自然科学基金资助项目(201801D121010)
Asymptotics and large time behavior of solutions to a type of time-space fractional wave equation
Received date: 2020-05-08
Online published: 2020-09-14
研究带分数阶 Laplace 算子的时间-空间分数阶偏微分方程解的渐近性, 其中时间分数阶导数是在 Caputo 导数意义下, 其导数阶 $\alpha\in(1,2)$. 利用 Fox $H$-函数的性质和 Young 不等式给出了解的梯度估计, 并且研究了其长时间行为.
关键词： Caputo 导数; 分数阶 Laplace 算子; 渐近性; 长时间行为
李志强 . 时空分数阶波方程解的渐近性与长时间行为[J]. 上海大学学报(自然科学版), 2021 , 27(6) : 1149 -1161 . DOI: 10.12066/j.issn.1007-2861.2257
This study investigates the asymptotic behaviors of a solution to time-space fractional partial differential equation with the fractional Laplacian, where the time fractional derivative is in the sense of Caputo, with the order $\alpha\in(1,2)$. By using the properties of the Fox $H$-function and Young's inequality, gradient estimates and large time behavior of the solution are obtained.
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