【作者】 李丹；

【导师】 李中平；

【作者基本信息】 西华师范大学 ， 应用数学， 2022， 硕士

【摘要】 本文研究了两类具有间接信号和logistic源的趋化模型解的全局存在性,解的全局有界性和渐近行为。本文内容安排如下:第一章主要概述了趋化模型的背景、研究现状及本文主要研究的内容。第二章主要在齐次Neumann边界条件下考虑一类具有间接信号消耗和logistic源的趋化模型其中（?）是边界光滑的有界区域。参数ρ＞0,μ＞0,l＞1和δ＞0,函数（？）。本章主要证明了两个结论:（1）如果（？）,则这个模型拥有一个全局存在解。（2）如果（？）,当t→∞时,全局有界解（u,v,w）满足第三章主要考虑具有间接信号产生和logistic源的抛物-椭圆-椭圆趋化模型其中参数μ＞0,y＞1,（？）是边界光滑的有界区域,D,S∈C²（[0,∞）)满足（？）且a₀＞0,b₀＞0,α,β∈R。本章主要证明如果β≤y-1,非负经典解（u,v,w）是全局有界的;如果μ＞0是充分大的,那么全局有界解（u,v,w）满足第四章对本文进行总结,并给出展望。更多还原

【Abstract】 This paper studies the global existence,global boundedness and asymptotic behavior of solutions to two types of chemotaxis models with indirect signal and logistic source.The content of this paper is arranged as follows:The first chapter mainly summarizes the background of the chemotaxis model,the research status and the main research content of this paper.Chapter 2 considers a class of chemotaxis models with indirect signal consumption and logistic source under homogeneous Neumann boundary conditionswhere （?） is a bounded region with smooth boundary.Parameters ρ＞0,μ＞0,l＞1 and δ＞0,and the function （?）.This chapter mainly proves two conclusions :（1）if （?）,then the model has a global existence solution.（2）if （?）,the globally bounded solution（u,v,w）satisfiesIn chapter 3,the parabolic-elliptic-elliptic chemotaxis model with indirect signal generation and logistic source is consideredwhere parameters μ＞0,y＞1,（？） is a bounded region with smooth boundary,D,S∈C²（[0,∞）)satisfy （?） and a₀＞0,b₀＞0,α,β∈R.This chapter mainly proves that if β≤y-1,the nonnegative classical solution（u,v,w）is globally bounded;if μ＞0 is sufficiently large,then the solution（u,v,w）satisfiesThe fourth chapter summarizes the thesis and give the prospect.更多还原