数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 156-168.doi: 10.1007/s10473-023-0110-y

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BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS*

Haiyang Jin, Kaiying Xu   

  1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2021-08-05 修回日期:2022-07-07 发布日期:2023-03-01
  • 通讯作者: †Haiyang JIN.E-mail: mahyjin@scut.edu.cn
  • 基金资助:
    *NSF of China (11871226), Guangdong Basic and Applied Basic Research Foundation (2020A1515010140 and 2022B1515020032), Guangzhou Science and Technology Program (202002030363).

BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS*

Haiyang Jin, Kaiying Xu   

  1. School of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2021-08-05 Revised:2022-07-07 Published:2023-03-01
  • Contact: †Haiyang JIN.E-mail: mahyjin@scut.edu.cn
  • About author:Kaiying Xu, E-mail: 201920127920@mail.scut.edu.cn
  • Supported by:
    *NSF of China (11871226), Guangdong Basic and Applied Basic Research Foundation (2020A1515010140 and 2022B1515020032), Guangzhou Science and Technology Program (202002030363).

摘要: This paper is concerned with the parabolic-parabolic-elliptic system {ut=Δuχ(uv)+ξ1(umw),xΩ,t>0,vt=Δv+ξ2(vw)+uv,xΩ,t>0,0=Δw+u1|Ω|Ωu,Ωw=0,xΩ,t>0,uν=vν=wν=0,xΩ,t>0,u(x,0)=u0(x),v(x,0)=v0(x),xΩ in a bounded domain ΩRn with a smooth boundary, where the parameters χ,ξ1,ξ2 are positive constants and m1. Based on the coupled energy estimates, the boundedness of the global classical solution is established in any dimensions (n1) provided that m>1.

关键词: boundedness, convection, chemotaxis, tumor invasion

Abstract: This paper is concerned with the parabolic-parabolic-elliptic system {ut=Δuχ(uv)+ξ1(umw),xΩ,t>0,vt=Δv+ξ2(vw)+uv,xΩ,t>0,0=Δw+u1|Ω|Ωu,Ωw=0,xΩ,t>0,uν=vν=wν=0,xΩ,t>0,u(x,0)=u0(x),v(x,0)=v0(x),xΩ in a bounded domain ΩRn with a smooth boundary, where the parameters χ,ξ1,ξ2 are positive constants and m1. Based on the coupled energy estimates, the boundedness of the global classical solution is established in any dimensions (n1) provided that m>1.

Key words: boundedness, convection, chemotaxis, tumor invasion