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Boundedness and finite-time blow-up in a chemotaxis system with nonlinear signal production
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2020-10-20 , DOI: 10.1016/j.nonrwa.2020.103237
Wanwan Wang , Yuxiang Li

The purpose of this paper is to study radially symmetric solutions of a parabolic–elliptic chemotaxis system (0.1)ut=Δu(f(u)v)inBR×(0,+),0=Δvμ(t)+g(u)inBR×(0,+)subject to homogeneous Neumann boundary conditions, where BR=BR(0)Rn with n1, R>0 and μ(t)=1|BR|BRg(u(x,t))dx denotes the time-dependent spatial mean of g(u). The chemosensitivity f and nonlinear signal production g are suitably regular functions. We show that the blow-up phenomenon of radially symmetric solution (u,v) of (0.1) in finite time for some initial datum u0, when f(ξ)Kξk and g(ξ)Lξl for all ξ1 with K,k,L,l>0 and k+l1>2n. However, system (0.1) admits a global bounded classical solution for arbitrary initial datum when f(ξ)Kξk and g(ξ)Lξl for all ξ1 with k+l1<2n.



中文翻译:

具有非线性信号产生的趋化系统中的有界性和有限时间爆炸

本文的目的是研究抛物线-椭圆趋化系统的径向对称解(0.1)üŤ=Δü-Füv[R×0+0=Δv-μŤ+Gü[R×0+服从齐次Neumann边界条件,其中 [R=[R0[Rññ1个[R>0μŤ=1个|[R|[RGüXŤdX 表示随时间变化的空间均值 Gü。化学敏感性F 和非线性信号产生 G是适当的常规函数​​。我们证明了径向对称解的爆炸现象üv 初始时间内在有限时间内的(0.1) ü0, 什么时候 FξķξķGξ大号ξ 对所有人 ξ1个ķķ大号>0ķ+-1个>2ñ。但是,系统(0.1)在以下情况下接受任意初始基准的全局有界经典解FξķξķGξ大号ξ 对所有人 ξ1个ķ+-1个<2ñ

更新日期:2020-10-29
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