The steady states and convergence to equilibria for a 1‐D chemotaxis model with volume‐filling effect
The steady states and convergence to equilibria for a 1‐D chemotaxis model with volume‐filling effect
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DOI：
10.1002/mma.1147
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发表时间：
2009-04
影响因子：
2.9
通讯作者：
Yanyan Zhang
中科院分区：
文献类型：
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作者：
Yanyan Zhang
我们考虑了由helen和Painter介绍的具有体积填充效应的趋化模型。他们还证明了无边界紧致黎曼流形整体解的存在性。此外，Wrzosek证明了在W1， p（Ω∧∈n）， p>n， p≠2中的全局吸引子的存在性。他还证明了ω极限集由正则平稳解组成。在本文中，我们证明了1 - D平稳问题最多有无穷可数个正则解。此外，我们表明，当t→∞时，1‐D进化问题的解收敛到W1， p， p大于或等于2的平衡。版权所有©2009 John Wiley & Sons， Ltd
We consider a chemotaxis model with volume‐filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W1, p(Ω⊂ℝn), p>n, p⩾2, was proved by Wrzosek. He also proved that the ω‐limit set consists of regular stationary solutions. In this paper, we prove that the 1‐D stationary problem has at most an infinitely countable number of regular solutions. Furthermore, we show that as t→∞ the solution of the 1‐D evolution problem converges to an equilibrium in W1, p, p⩾2. Copyright © 2009 John Wiley & Sons, Ltd.