Reduction of reaction diffusion system and asymptotic analysis

1.对于趋化性增长模型（1）在Neumann边界条件下，利用奇异极限分析方法，在通道区域上得到了行波解的存在性及其稳定性;（2）在三维空间中，利用约化系统得到了对称定态解的存在性及其稳定性;（3）在奇异灵敏度函数的情况下，得到了时间全局非负解和有限维指数吸引子的存在性;（4）非负常数解的不稳定性和指数吸引子的维数的发散，由于趋化效应的增加2。对于吸附诱导相变模型（1）在有限段上周期边界条件下时间整体非负解和有限维指数吸引子的存在性（2）在具有C^2类边界的二维有限区域或凸区域上Newmann边界条件下时间整体非负解和有限维指数吸引子的存在性（3）在Newmann边界条件下，由于正方形区域中非负常数解的分支，条纹和六边形定态解的存在性3.对于森林运动学模型（1）引入了三种Ω极限集并研究了它们的基本性质

1. For the chemotaxis growth model(1) Existence of a traveling front solution and its stability in a channel domain with Neumann boundary condition by using singular limit analysis(2) Existence of a symmetric stationary solution and its stability in 3 dimensional space by using the reduction system(3) Existence of time global non-negative solution and finite dimensional exponential attractor in the case of singular sensitivity function(4) Instability of the non-negative constant solution and divergence of the dimension of the exponential attractor due to the increases of the chemotaxis effect2. For the adsorbate-induced phase transition model(1) Existence of time global non-negative solution and finite dimensional exponential attractor under periodic boundary condition in a finite segment(2) Existence of time global non-negative solution and finite dimensional exponential attractor under Newmann boundary condition in 2dimensional finite domain with C^2 class boundary or convex domain(3) Existence of the stripe and hexagonal stationary solutions due to the bifurcation from non-negative constant solution in the square domain with Newmann boundary condition3. For the forest kinematic model(1) Introduction of three kinds of omega limit sets and investigation of the basic property of these limit sets