Degn-Harrison反应扩散系统平衡态解的定性分析  

Qualitative analysis of steady-state solutions for the Degn-Harrison reaction-diffusion system

作　　者：李兵方[1] 李艳玲[2] LI Bing-fang;LI Yan-ling(Department of Basic Course, Shaanxi Railway Institute, Weinan 714000, China;College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, China)

机构地区：[1]陕西铁路工程职业技术学院基础课部,陕西渭南714000 [2]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《陕西科技大学学报》2021年第4期175-181,共7页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(61872227).

摘　　要：在齐次Neumann边界条件下研究一类Degn-Harrison反应扩散系统的平衡态问题.首先利用极大值原理,给出正解的先验估计.其次利用Hölder不等式、Poincaré不等式及Cauchy不等式,给出正解的相关不等式性质,并得到非常数正解的三个不存在性条件.最后利用分歧理论,在扩散系数满足一定条件时建立分歧正解的存在性.结果表明,如果营养物扩散太慢、反应区域太小或者氧气扩散太快,系统不会出现非齐次的空间结构;而在一定扩散条件下,系统将呈现空间分布不均匀的状态.The steady-state problem for the Degn-Harrison reaction-diffusion system subject to Neumann boundary conditions is considered.By maximum principle,Hölder inequality and Poincaréinequality,a priori estimate and some inequality properties of steady-state solutions are obtained.Meanwhile,three conditions of non-existence of non-constant positive steady-state solutions are given.Moreover,the existence of positive bifurcation solution is established using bifurcation theory.The results indicate that non-homogeneously spatial structures do not exist if the substance diffuses slowly,the reaction region is small,or the oxygen diffuses quickly.But,a state of non-homogeneous spatial distribution will be presented if some diffusion conditions are satisfied.

关 键 词：Degn-Harrison反应扩散系统 先验估计 不存在性 分歧 

分 类 号：O175.26[理学—数学]