带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为

Abstract

Abstract:

This paper studies the attraction-repulsion chemotaxis system with logistic source u_t=Δu-▽·(u▽v)+μ₁u(1-u), 0=Δv+w-v, w_t=Δw+▽·(w▽z)+μ₂w(1-w), 0=Δz-z+u, in bounded domain Ω⊂R^N, N≥1, subject to the homogeneous Neumann boundary conditions, and μ₁,μ₂>0. It is proved that for any nonegative initial data u₀(x),w₀(x)∈C(Ω), the solution (u(·,t),v(·,t),w(·,t),z(·,t)) is globally bounded. Furthermore, if μ₁,μ₂>(1)/(16), then (u(·,t),v(·,t),w(·,t),z(·,t)) converges asymptotically to the constant equilibrium (1,1,1,1) in the L^∞-norm as t→∞.

Key words: Attraction-repulsion, Chemotaxis, Logistic source, Boundedness, Asymptotic behavior

CLC Number:

O175.29

Gao Xinchun, Zhou Jian, Tian Miaoqing. Global Boundedness and Asymptotic Behavior in an Attraction-Repulsion Chemotaxis System with Logistic Source[J].Acta mathematica scientia,Series A, 2017, 37(1): 113-121.

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Global Boundedness and Asymptotic Behavior in an Attraction-Repulsion Chemotaxis System with Logistic Source

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