| 分歧理论在一类半线性偏微分方程中的应用 |
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| 引用本文： | 祝贺,苏正君.分歧理论在一类半线性偏微分方程中的应用[J].沈阳化工学院学报,2009,23(1):89-91. |
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| 作者姓名： | 祝贺 苏正君 |
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| 作者单位： | 1. 沈阳化工学院数理系,辽宁,沈阳,110142
2. 辽阳职业学院计算机系,辽宁,辽阳,111000 |
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| 摘 要： | 利用经典局部、全局分歧定理，考虑一类具有第一类边值条件的一类反应扩散方程果蝇模型。研究了解全局存在性，并利用偏微分方程的最大值原理和泛函分析的谱理论，证明从常值解附近分歧出来的分歧解关于分歧参数单调增加的，从而证明方程的解关于参数存在唯一性．
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| 关 键 词： | 果蝇模型 反应扩散方程 稳态解分歧 全局存在性 解的单调性 |
Applications of Bifurcation Theory in a Semilinear Partial Differential Equations |
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| ZHU He,SU Zheng-jun.Applications of Bifurcation Theory in a Semilinear Partial Differential Equations[J].Journal of Shenyang Institute of Chemical Technolgy,2009,23(1):89-91. |
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| Authors: | ZHU He SU Zheng-jun |
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| Affiliation: | ZHU He, SU Zheng-jun (1. Shenyang University of Chemical Technology, Shenyang 110142, China; 2. Liaoyang Professional Technology Institute, Liaoyang 111000, China) |
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| Abstract: | In this paper, a kind of Nichloson blowflies equation subject to Dirichlet boundary condition were considered by using standard local and global bifurcation theorems. This model is of a reaction-diffusion equation. Consider the global existence of the solution of this system, where Maximal Principals in PDEs, spectral theory in Functional analysis are frequently used. Furthermore, we also prove the uniqueness of the solution of this system by showing that the solution curve is monotone with respect to the bifurcation parameter. |
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| Keywords: | nicolson blowfilies reaction-diffusion equation steady state bifurcations global existence monoticity |
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