趋化运动双曲模型弱解的存在唯一性

Existence and Uniqueness of Weak Solutions for a Hyperbolic Chemotaxis Model

研究了一维空间上趋化运动的一个双曲模型,相对于传统的描述微粒群整体运动的Goldstein-Kac模型,我们提出的模型则描述单个微粒的运动,在假设微生物的运动速度是常数,并且s的生产和消退是线性的基础上,得到了弱解的局部存在唯一性.

We study a hyperbolic model for chemotaxis in one space dimension.Comparing with the generalized Goldstein-Kac model which describes the movement of total population,the model we present here explains the movement of each particle.We assume the speed and turning rates are constant,and the reproduction and degradation of s is linear.Local existence and uniqueness for weak solutions are shown.