时空分数阶推广Keller-Segel方程解的存在性  

The existence of solutions to the generalized fractional time-space Keller-Segel equations

作　　者：姜自文 王丽真 Jiang Ziwen;Wang Lizhen(School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2020年第3期312-322,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11771352);陕西省自然科学基金(2020JM431).

摘　　要：研究了时空分数阶推广Keller-Segel方程的mild解的存在性.运用Mittag-leffler函数的渐近行为产生的压缩性得到分数阶扩散方程解算子的估计,结合不动点定理,得到了时空分数阶推广Keller-Segel方程mild解的局部存在性,在给定小初值的条件下得到了方程全局mild解的存在性.In this paper,the existence of the mild solutions to the fractional time-space generalized Keller-Segel equations is investigated.Based on the contraction properties that follow from the asymptotic behavior of the Mittag-Leffler functions to obtain the estimates for the solution operators of the homogeneous fractional diffusion equations and the fixed point theorem,the local existence of the mild solutions is constructed and the global existence of the mild solutions is also established with small data.

关 键 词：时空分数阶推广Keller-Segel方程 MILD解 存在性 

分 类 号：O175.2[理学—数学]