Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1382-1395.

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Global Boundedness in a Chemotaxis-Haptotaxis Model with Nonlinear Diffusion and Signal Production

Zhe Jia1,Zuodong Yang2,3,*()   

  1. 1 School of Mathematics and Statistics, Linyi University, Shandong Linyi 276005
    2 School of Teacher Education, Nanjing Normal University, Nanjing 210097
    3 School of Teacher Education, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2020-03-24 Online:2021-10-26 Published:2021-10-08
  • Contact: Zuodong Yang E-mail:jin@263.net
  • Supported by:
    the NSFC(11571093);the NSF of Jiangsu Education Commission(19KJB110016);the Scientific Research Foundation of Linyi University(LYDX2020BS014)

Abstract:

This paper is concerned with an initial-boundary value problem for the following chemotaxis-haptotaxis model under homogenous Neumann boundary condition in a bounded domain $ \Omega \subset \mathbb{R} ^{3} $, with $ \chi, \xi, \mu,\lambda,$ $\gamma >0$, $k>1$, $a \in \mathbb{R} $, and $D(u)\geq C_{D} (u+1)^{m-1}$ for $C_{D}>0, m\in \mathbb{R} $. It is shown that(i) For $0<\gamma\leq\frac{2}{3}$, if $\alpha>\gamma-k+1$ and $\beta>1-k$, there is a classical solution $(u, v, w)$ which is globally bounded to the above problem.(ii) For $\frac{2}{3}<\gamma\leq1$, if $\alpha>\gamma-k+\frac{1}{e}+1$ and or $\alpha>\gamma-k+1$ and there is a classical solution $(u, v, w)$ which is globally bounded to the above problem.

Key words: Global existence, Boundedness, Chemotaxis-haptotaxis, Nonlinear diffusion

CLC Number: 

  • O175.26
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