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一类反应扩散方程组平衡解的局部分歧及稳定性 被引量：4

Local bifurcation and stability of steady state solutions of a reaction-diffusion systems
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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.
作者 李津 李艳玲
机构地区 陕西师范大学数学与信息科学学院
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 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)
关键词 局部分歧 半平凡平衡解 稳定性 local bifurcation semi-trivial steady-state solution stability
分类号 O175.26 [理学—基础数学]
  • 相关文献

参考文献9

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二级参考文献13

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共引文献16

同被引文献31

  • 1黑力军.一类具有扩散的互惠共食系统的存在性和全局吸引性[J].应用数学,2005,18(4):594-602. 被引量：1
  • 2郑秋红,李艳玲.一类带饱和项互惠模型平衡态正解的存在性[J].陕西师范大学学报（自然科学版）,2006,34(3):14-18. 被引量：2
  • 3曾宪忠,周树清.带有交叉扩散的捕食模型的非常数正稳态解的存在性[J].应用数学学报,2006,29(6):1063-1079. 被引量：3
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引证文献4

二级引证文献7

陕西师范大学学报（自然科学版）
2008年 第2期

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