一类反应扩散方程组平衡解的局部分歧及稳定性  

Local bifurcation and stability of steady state solutions of a reaction-diffusion systems

作　　者：李津[1] 李艳玲[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2008年第2期15-18,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10571115)

摘　　要：研究了一类半线性反应扩散方程组在带Dirichlet边界条件下正解的存在性及稳定性.用单调解的方法给出了此解的估计,利用局部分歧理论研究了当n=1和n≠1两种情况下模型在半平凡平衡态解(θa,0)上出现的局部分歧现象,并证明了在分歧点(■,aθ,0)附近存在正解;利用稳定性理论得出当n=1时,若c、d异号,该共存解稳定;若c、d同号时,该共存解不稳定.The existence and stability of positive solutions of a semi-linear reaction-diffusion system with Dirichlet boundary conditions are studied. An estimate of the solutions is given by the monotone method; by means of local bifurcation theory, the system bifurcations at semi-trivial solutions for two cases（ n = 1 and n≠1） are studied. It is proved that positive solutions exist in some neighborhoods of （λ,θa,0）. It is proved that when n = 1 and cd 〈0, the positive solution is stable.

关 键 词：局部分歧 半平凡平衡解 稳定性 

分 类 号：O175.26[理学—数学]