| 时空分数阶波方程解的渐近性与长时间行为 |
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| 引用本文： | 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. |
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| 作者姓名： | 李志强 |
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| 作者单位： | 1.上海大学 理学院, 上海 200444;2.吕梁学院 数学系, 山西 吕梁 033001 |
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| 基金项目： | 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) |
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| 摘 要： | 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.
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| 关 键 词： | Caputo 导数 分数阶 Laplace 算子 渐近性 长时间行为 |
| 收稿时间： | 2020-05-08 |
Asymptotics and large time behavior of solutions to a type of time-space fractional wave equation |
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| LI Zhiqiang.Asymptotics and large time behavior of solutions to a type of time-space fractional wave equation[J].Journal of Shanghai University(Natural Science),2021,27(6):1149-1161. |
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| Authors: | LI Zhiqiang |
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| Institution: | 1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Department of Mathematics, Lüliang University, Lüliang 033001, Shanxi, China |
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| Abstract: | 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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| Keywords: | Caputo derivative fractional Laplacian asymptotic behavior large time behavior |
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