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BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS*
Haiyang Jin, Kaiying Xu
Acta mathematica scientia,Series B. 2023, 43 (1):
156-168.
DOI: 10.1007/s10473-023-0110-y
This paper is concerned with the parabolic-parabolic-elliptic system {ut=Δu−χ∇⋅(u∇v)+ξ1∇⋅(um∇w),x∈Ω,t>0,vt=Δv+ξ2∇⋅(v∇w)+u−v,x∈Ω,t>0,0=Δw+u−1|Ω|∫Ωu,∫Ωw=0,x∈Ω,t>0,∂u∂ν=∂v∂ν=∂w∂ν=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω in a bounded domain Ω⊂Rn with a smooth boundary, where the parameters χ,ξ1,ξ2 are positive constants and m≥1. Based on the coupled energy estimates, the boundedness of the global classical solution is established in any dimensions (n≥1) provided that m>1.
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