Properties Of Two Oxygen-Consumption Chemotaxis Models With Logistic Source

Chemotaxis models are partial differential systems used to describe chemotaxis phenomena in nature.If the proliferation and death of cells themselves are considered,it is necessary to research a chemotaxis model with logistic source terms.This dissertation mainly studies the properties of two oxygen-consuming chemotaxis models with logistic source.This dissertation mainly studies the following initial-boundary value problem:where(?)(N?N)is a bounded domain with smooth boundary,parameter ?>0,v represents the normal vector outside the unit on(?)?.The unknown function u(x,t)is the cell density and v(x,t)is the chemical signal concentration,f(u)is logistic source.This dissertation is mainly divided into the following parts:The preface introduces the biological background of chemotaxis models and the research progress and results of some chemotaxis models related to the problem we will study.The first chapter is the preliminaries which include some necessary lemmas.In chapter 2,we prove that when the logistic source term is f(u)=ru-?u2,the integral of the first component of the global classical solution(u,v)has a positive lower bound in the model(*).In chapter 3,we study the global existence of the classical solutions to the initial-boundary value problem when the logistic source term is f(u)=u(a₀-a₁u-a₂?_?u).