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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (4): 40-47.doi: 10.6040/j.issn.1671-9352.0.2016.330

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Keller-Segel型交叉扩散方程组柯西问题解的逐点估计

段双双,钱媛媛   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241000
  • 收稿日期:2016-07-10 出版日期:2017-04-20 发布日期:2017-04-11
  • 作者简介:段双双(1990— ), 女, 硕士研究生, 研究方向为偏微分方程. E-mail:duanss0517@126.com
  • 基金资助:
    国家自然科学基金资助项目(11301006);安徽省自然科学基金资助项目(1408085MA01);安徽高校省级自然科学研究重点项目(KJ2015A117)

The pointwise estimates of solutions to the Cauchy problem of Keller-Segel equations with cross-diffusion

DUAN Shuang-shuang, QIAN Yuan-yuan   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China
  • Received:2016-07-10 Online:2017-04-20 Published:2017-04-11

摘要: 研究了一类Keller-Segel型交叉扩散方程组的柯西问题。 利用Green函数的方法, 得到带有小初值的柯西问题解的逐点估计, 以及解在W s,p(Rn)空间中的衰减性质。

关键词: Green 函数, Keller-Segel 模型, 衰减率, 逐点估计, 趋化性

Abstract: We consider the Canchy problem for a class of Keller-Segel equations with cross-diffusion. By utilizing the method of Greens function, we obtain the pointwise estimates of solutions to the Cauchy problem for small initial data, and the W s,p(1≤p≤∞) decay properties of solutions.

Key words: Greens function, decay rates, Keller-Segel model, pointwise estimates, chemotaxis

中图分类号: 

  • O175.2
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