| 王曦,刘祖汉,周玲.具不同分数阶扩散趋化模型的衰减估计[J].数学年刊A辑,2020,41(2):175~200 |
| 具不同分数阶扩散趋化模型的衰减估计 |
| Temporal Decay for the Chemotaxis System Involving Different Fractional Powers in Higher Dimensions |
| Received:November 12, 2017 Revised:April 04, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0013 |
| 中文关键词: 趋化模型, 分数阶 Laplacian, 古典解, 衰减估计 |
| 英文关键词:Chemotaxis system, Fractional Laplacian, Global classical solution, Temporal decay |
| 基金项目:国家自然科学基金(No.\,11771380, No.\,11401515) |
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| 中文摘要: |
| 研究了生物学中具有分数阶扩散的 Keller-Segel模型. 该模型是由两个分数阶抛物方程和一个经典抛物方程组成. 在小初值条件下,利用[李大潜, 陈韵梅. 非线性发展方程 [M]. 北京: 科学出版社, 1999.]中的能量方法,作者建立了该模型古典解的全局存在性及最优的衰减估计, 得到了u, v 及 ?ψ高阶导数的衰减估计. |
| 英文摘要: |
| This paper deals with a fractional Keller-Segel model arising from biology, which involves two parabolic equations with fractional Laplacians and a classical parabolic equation. The global existence result and the optimal temporal decay estimates of the classical solution to the fractional Keller-Segel system are obtained by pure energy method in [Li T, Chen Y. Nonlinear evolution equation, Beijing: Science Press, 1999 (in Chinese).] based on the assumption of smallness initial conditions. More precisely, the authors derive the optimal decay rates of the higher-order spatial derivatives ofu, v 及 ?ψ. |
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