Reduction of reaction diffusion system and asymptotic analysis

反应扩散系统的约简与渐近分析

基本信息

批准号：
17540125
负责人：
TSUJIKAWA Tohru
金额：
$ 2.03万
依托单位：
University of Miyazaki
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540125/
关键词：
Exponential Attractor Reaction diffusion equation Singular limit Squeezing property Bifurcation Weakly interaction Stability Pattern formation Interface analysis Weakly Interaction Traveling front solution Kinematic model Exponenti

项目摘要

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

1。对于趋化性生长模型（1），通过使用单数极限分析（2）存在对称固定溶液的存在（2），使用降低溶液（3）使用时间固定系统（3），使用时间固定系统（3）存在时间全球非维度溶液和有限态度的稳定性稳定性的态度（3）由于趋化效应的增加，溶液和指数吸引子的尺寸差异。对于吸附物诱导的相变模型（1）时间全球非负溶液的存在和有限的尺寸指数吸引膜在有限段（2）存在的周期性边界条件下（2）全球非全面解决方案和有限尺寸指数的吸引子在Newmann在2 ddimentim firite domain clastiental clastiental and Clastiental and clande and contriental and contriental and contriend and dromain and dromain（3）中的存在（3），或者存在。固定溶液是由于具有Newmann边界条件的正方形域中非负恒定溶液分叉3。对于森林运动学模型（1）引入三种欧米茄限制集和对这些极限集的基本属性的调查