Existence And Uniqueness Of Weak Solutions For A Hyperbolic Models For Chemotaxis

In this paper,we study a hyperbolic model for chemotaxis in one space dimension.chemotaxis movement is a widespread phenomenon in biological systems,hyperbolic models for chemotaxis can describe this phenomenon quite well in some extent.In chapter one,we shall introduce the background and mathematical form of hyperbol-ic model for chemotaxis.In chapter 2,we shall give some basic knowledge to prove the main conclusions,including maximum principle,fixed point theorem and General Sobolev inequalities.In chapter 3,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.