Chemotaxis model with nonlocal nonlinear reaction in the whole space
Chemotaxis model with nonlocal nonlinear reaction in the whole space
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DOI：
10.3934/dcds.2018222
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
S. Bian;Li Chen;E. Latos
中科院分区：
文献类型：
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作者：
S. Bian;Li Chen;E. Latos
研究了一类具有非局部源的抛物-椭圆趋化系统。证明了该初值问题存在唯一的一致有界整体解。在这里，我们以使其标度和扩散项重合的方式识别非线性反应和聚集的指数状态（见引言）。与经典的KS模型（无源项）相比，在对初始数据没有任何限制的情况下，能量估计给出了非线性项的自然条件，从而使解不存在爆破.
This paper deals with a parabolic-elliptic chemotaxis system with nonlocal type of source in the whole space. It's proved that the initial value problem possesses a unique global solution which is uniformly bounded. Here we identify the exponents regimes of nonlinear reaction and aggregation in such a way that their scaling and the diffusion term coincide (see Introduction). Comparing to the classical KS model (without the source term), it's shown that how energy estimates give natural conditions on the nonlinearities implying the absence of blow-up for the solution without any restriction on the initial data.