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Volume 34, Issue 1
Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General Memory Term

Yingdong Wu, Shaohua Wu, Xin Cheng & Lei Liu

DOI: 10.4208/jpde.v34.n1.5

J. Part. Diff. Eq., 34 (2021), pp. 67-82.

Published online: 2021-01

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  • Abstract

In this paper, we discuss the local existence of weak solutions for a parabolic system modelling chemotaxis with memory term, and we show the finite-time blow-up and chemotactic collapse for this system. The main methods we used are the fixed point theorem and the semigroup theory.

  • Keywords

parabolic system, chemotaxis, memory term, fixed point theorem, blow-up.

  • AMS Subject Headings

35A01, 35A02, 35K51

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

15755508002@163.com (Yingdong Wu)

s.h.wu@163.com (Shaohua Wu)

chengxin021@whu.edu.cn (Xin Cheng)

liulei95@whu.edu.cn (Lei Liu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-67, author = {Wu , YingdongWu , ShaohuaCheng , Xin and Liu , Lei}, title = {Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General Memory Term}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {1}, pages = {67--82}, abstract = {

In this paper, we discuss the local existence of weak solutions for a parabolic system modelling chemotaxis with memory term, and we show the finite-time blow-up and chemotactic collapse for this system. The main methods we used are the fixed point theorem and the semigroup theory.

}, issn = {2079-732X}, doi = {https://doi.org/ 10.4208/jpde.v34.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/18555.html} }
TY - JOUR T1 - Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General Memory Term AU - Wu , Yingdong AU - Wu , Shaohua AU - Cheng , Xin AU - Liu , Lei JO - Journal of Partial Differential Equations VL - 1 SP - 67 EP - 82 PY - 2021 DA - 2021/01 SN - 34 DO - http://doi.org/ 10.4208/jpde.v34.n1.5 UR - https://global-sci.org/intro/article_detail/jpde/18555.html KW - parabolic system, chemotaxis, memory term, fixed point theorem, blow-up. AB -

In this paper, we discuss the local existence of weak solutions for a parabolic system modelling chemotaxis with memory term, and we show the finite-time blow-up and chemotactic collapse for this system. The main methods we used are the fixed point theorem and the semigroup theory.

Wu , YingdongWu , ShaohuaCheng , Xin and Liu , Lei. (2021). Finite-Time Blow-Up and Local Existence for Chemotaxis System with a General Memory Term. Journal of Partial Differential Equations. 34 (1). 67-82. doi: 10.4208/jpde.v34.n1.5
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