Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
复制标题
消耗趋化剂的三维趋化系统中大数据解决方案的最终平滑性和稳定性
DOI：
10.1016/j.jde.2011.07.010
复制
发表时间：
2012-02-01
影响因子：
2.4
通讯作者：
Winkler, Michael
中科院分区：
文献类型：
--
作者：
Tao, Youshan;Winkler, Michael
本文讨论了{u(T)=Delta u-del的正解。(U Del V)，x是Omega，t>；0的元素，v(T)=Delta v-uv，x是Omega，t>；0的齐次Neumann边界条件下R(3)的有界凸区域Omega子集上的光滑边界，证明了对于任意大的初值，该问题至少存在一个整体弱解，且存在T>；0使得(u，v)在Omega x(T，无穷)中是有界光滑的.此外，我们还断言这种解在较大的时间范围内逼近空间不变的平衡。(C)2011 Elsevier Inc.保留所有权利。
This paper deals with positive solutions of{ u(t) = Delta u - del . (u del v), x is an element of Omega, t > 0,v(t) = Delta v - uv, x is an element of Omega, t > 0,under homogeneous Neumann boundary conditions in bounded convex domains Omega subset of R(3) with smooth boundary.It is shown that for arbitrarily large initial data, this problem admits at least one global, weak solution for which there exists T > 0 such that (u, v) is bounded and smooth in Omega x (T, infinity). Moreover, it is asserted that such solutions approach spatially constant equilibria in the large time limit. (C) 2011 Elsevier Inc. All rights reserved.