Existence and stability of steady-state solutions of reaction–diffusion equations with nonlocal delay effect
Existence and stability of steady-state solutions of reaction–diffusion equations with nonlocal delay effect
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DOI：
10.1007/s00033-021-01474-1
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
W. Zuo;Junping Shi
中科院分区：
文献类型：
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作者：
W. Zuo;Junping Shi
研究了一类具有齐次Dirichlet边界条件的一般的反应扩散方程。通过研究一个等价的无非局部时滞结构的反应扩散方程组，利用局部和全局分歧理论，证明了正平衡解的存在性和稳定性.的全局结构的一组稳定状态的特点是根据类型的非线性和扩散系数。我们的一般结果被应用到扩散Logistic增长模型和Nicholson的苍蝇型模型。
A general reaction–diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady-state solutions are proved via studying an equivalent reaction–diffusion system without nonlocal and delay structure and applying local and global bifurcation theory. The global structure of the set of steady states is characterized according to type of nonlinearities and diffusion coefficient. Our general results are applied to diffusive logistic growth models and Nicholson’s blowflies-type models.