Global boundedness of solutions in a parabolic-parabolic chemotaxis system with singular sensitivity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:443

Article

Zhao, Xiangdong¹  Zheng, Sining¹ 

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

关键词: Keller-Segel system;    Chemotaxis;    Singular sensitivity;    Boundedness;   

DOI  :  10.1016/j.jmaa.2016.05.036

来源: Elsevier

【 摘 要 】

We consider a parabolic-parabolic Keller-Segel system of chemotaxis model with singular sensitivity: u(t) = Delta u-chi del.(u/v del v), v(t) = k Delta v - v+u under the homogeneous Neumann boundary condition in a smooth bounded domain Omega subset of R-n (n >= 2), with chi, k > 0. It is proved that for any k > 0, the problem admits global classical solutions, whenever chi is an element of (0,-k-1/2 +1/2 root(k - 1)(2) + 8k/n). The global solutions are moreover globally bounded if n <= 8. This shows a way the size of the diffusion constant k of the chemicals v affects the behavior of solutions. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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