一类具有logistic增长的消耗型趋化方程组的性质

Property of a Dissipative Chemotaxis System with Logistic Growth

摘要: 趋化性是指由空间中分布不均匀的物质所产生的化学信号刺激细胞或有机体的定向运动，其在免疫系统、胚胎发育、肿瘤生长、种群动态等生物学现象中起着重要的作用。趋化方程组(或趋化模型)是刻画趋化现象的偏微分方程组。因而，研究趋化方程组具有重要的理论价值和极强的现实意义。文章研究一类具有logistic源增长的消耗型趋化方程组在N维有界区域上的齐次Neumaan初边值问题的性质。利用半群理论、L^p估计、极大Sobolev正则性、Moser迭代等方法，证明了当logistic源项的非线性增长指标时，方程组存在唯一的全局有界经典解，其中，而，为极大Sobolev正则性中相应的常数。

Abstract: Chemotaxis is known to stimulate the biased motion of cells or organisms by chemical signals pro-duced by substances that are unevenly distributed in space, which has a crucial role in a wide range of biological phenomena such as immune system response, embryo development, tumor growth, population dynamics, etc. Chemotaxis equations (or chemotaxis system) are partial differential equations describing chemotaxis phenomena. Therefore, it is of great theoretical value and practical significance to study chemotaxis system. This article studies the properties of a homogeneous Neumann initial boundary value problem for an expendable chemotaxis system with logistic source growth in an N-dimensional bounded domain. Using semigroup theory, LP-estimation, maximal Sobolev regularity, Moser iteration and other methods, it is proved that when , then the system possesses a global classical solution which is bounded, where , and is a constant which is corresponding to the maximal Sobolev regularity.