项目名称: 几类拟线性偏微分方程组解的定性研究
项目编号: No.11501031
项目类型: 青年科学基金项目
立项/批准年度: 2016
项目学科: 数理科学和化学
项目作者: 徐茜
作者单位: 北京联合大学
项目金额: 18万元
中文摘要: 本项目主要致力于几类拟线性偏微分方程组解的定性研究。主要研究S-K-T型拟线性交错扩散方程组及多种拟线性趋化性交错扩散方程组在高维空间中整体解的存在性、一致有界性和爆破解的存在性;非常数平衡解(特别是具有尖峰、奇异结构的平衡解)在一维空间及高维空间的存在性、解的细致结构、渐近性及稳定性;一些非自治的交错扩散方程组竞争模型的非常数平衡解的存在性及稳定性。本项目所研究的课题均为国际相关领域的前沿研究课题,并且已有的一些经典方法不能直接应用于此类问题,我们将根据问题的特点寻找新的研究思路和研究方法,期望在得到完整深刻研究结果的同时,解释一些重要自然现象和实验结果。
中文关键词: 交错扩散方程组;平衡解;谱分析;存在性;稳定性
英文摘要: This research project will mainly study the qualitative research of solutions for several classes of partial differential equations with quasi-linear cross-diffusion ; which include the global existence、uniform boundness and the existence of blow up solutions for S-K-T competition models and chemotactic biological models with quasi-linear cross-diffusion in higher dimensional space; the existence and stability of nontrivial steady states with spiky or singular structure and the detailed structure and asymptotic behavior of solutions in one and higher dimensional space for several types of S-K-T competition models and chemotactic biological models with quasi-linear cross diffusion;the existence and stability of nonconstant solutions for some nonautonomous systems with cross-diffusion. The research topics which we will investigate are the pioneering problems in international related field.Some classical methods cannot be directly applied to such problems,so we will look for new ideas and methods according to the characteristic of the problems. We expect obtain deep results and explain some important phenomena and experimental results.
英文关键词: cross diffusion system;steady state;spectral analysis;existence;stability