On Local Existence And Blow-up Of A Moving Boundary Problem In 1-D Chemotaxis Model

The free boundary problem's application is extremely extensive on physics and bi-ology.This paper proves the existence and uniqueness of solutions for the free boundary chemotaxis problems.The thesis consists of three chapters.In chapter one,we shall introduce the back-ground of the chemotaxis problem and free boundary problems.In chapter two,we shall give some basic knowledge to prove the main conclusions,including the minimax princi-ple of classical solution for parabolic equation,comparison principle,Leray-Schauder's fixed point theorem and so on.In the last chapter,which is the main part of this pa-per.Firstly,the local existence and uniqueness of a chemotaxis model with a moving boundary are considered by the contraction mapping principle;in addition,the explicit expression for the moving boundary is formulated.At last,the finite-time blowup and chemotactic collapse of the solution for such kind of problem are discussed.