一类具有营养质的反应扩散模型正解及大时间行为

项目名称： 一类具有营养质的反应扩散模型正解及大时间行为

项目编号： No.11271236

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 吴建华

作者单位： 陕西师范大学

项目金额： 60万元

中文摘要： 在扩散恒化器模型研究中，本项目首次考虑模型中最大生长率与空间变量的关系，研究其正解存在唯一性、稳定性；首次建立转化率与营养质有关的扩散恒化器模型，并研究其正平衡解及周期解的性质；建立Ellner型扩散恒化器食物链模型并就其正平衡解、Hopf分歧解及其动力学行为进行研究；系统研究双营养质双微生物可替代型扩散恒化器模型正平衡解的存在性及大时间行为。本课题组长期从事扩散恒化器模型研究，在多营养质模型和具有质载的扩散恒化器模型的研究中形成了自己的研究方向。关注模型背景、巩固已有研究经验、借鉴相关反应扩散模型的研究方法并辅以数值模拟和数值分析，一直是本课题组取得进步的有效途径。本项目的研究既具有相当的难度，又是该领域的热点问题，也将提升扩散恒化器模型的研究层次, 提高青年研究人员学术水平，逐步形成我国学者在该领域的研究优势和特色。

中文关键词： 反应扩散模型；平衡解；周期解；存在唯一性；大时间行为

英文摘要： In the research of the diffusive chemostat, it is the first purpose that the existence, uniqueness and stability of positive steady-state solutions is studied in the case that the maximal growth rate is related to the spatial variable. Second, as to the case of the variable yield which is dependent on the nutrient,the diffusive chemostat model is first established, then the positive steady-state solution and the periodic solution is investigated. Next, we establish the food cycle model of the diffusive chemostat with Ellner type, and study positive steady-state solutions, the Hopf bifurcation and their dynamical behavior. Finally, we do the research systematically on the positive steady states and longtime behavior with respect to the diffusive chemostat with two nutrients and two sepcies in the substitutable case. In the past decades, our research group has been engaged in the chemostat model with diffusion, especially in the diffusive chemostat with multiple nutrients and the plasmid-brearing. The combination of the background of models,the mathematical analysis and simulation is always the effective way for us. The research of this project is the central and difficult area, and we hope that it is going to push both the research of the chemostat with diffusion and the academic level of young researchers to a h

英文关键词： reaction-diffusion model；steady-state solution；periodic solution；existence and uniqueness；longtime behavior