一类带反应项的 Othmer-Stevens型趋化模型解的存在性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1561-1571.

一类带反应项的 Othmer-Stevens型趋化模型解的存在性

武汉大学数学与统计学院武汉 430072

收稿日期:2007-12-30 修回日期:2008-09-15 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
国家自然科学基金(10471108)资助

Existence of Solution to Some Othmer-Stevens Chemotaxis System with Reaction Term

School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2007-12-30 Revised:2008-09-15 Online:2009-12-25 Published:2009-12-25
Supported by:
国家自然科学基金(10471108)资助

摘要/Abstract

摘要：

该文讨论了一类带反应项的Othmer-Stevens 型趋化模型的初边值问题
{∂u/∂t=D∨(u ∨ln u/Φ(x, t, w))+ f(x, t, u),

∂w/∂t=g(x, t, u, w),

u∨ln u/Φ(x, t, w) ?n^→=0.
证明了: 如果边界∂Ω ∈C^2+β, 函数Φ(x, t , w), f(x, t, u) 和 g(x, t, u, w)充分光滑,则该系统存在唯一解.

关键词: 趋化, Othmer-Stevens 模型, 紧算子, 不动点

Abstract:

In this paper, the authors study an initial-boundary value problem of Othmer-Stevens chemotaxis system with reaction term in the master equation

{∂u/∂t=D∨(u ∨ln u/Φ(x, t, w))+ f(x, t, u),

∂w/∂t=g(x, t, u, w),

u∨ln u/Φ(x, t, w) ?n^→=0.
They prove that there exists a unique solution if the boundary ∂Ω ∈^C2+β, the functions Φ(x, t, w), f(x, t, u) and g(x, t, u, w) are sufficiently smooth.

Key words: Chemotaxis, Othmer-Stevens model, Compact operator, Fixed point

中图分类号:

35K57

李俊锋, 刘伟安. 一类带反应项的 Othmer-Stevens型趋化模型解的存在性[J]. 数学物理学报, 2009, 29(6): 1561-1571.

LI Jun-Feng, LIU Wei-An. Existence of Solution to Some Othmer-Stevens Chemotaxis System with Reaction Term[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1561-1571.

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