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A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2020-07-16 , DOI: 10.1016/j.nonrwa.2020.103191
Abir Abbad , Salem Abdelmalek , Samir Bendoukha , Gaetana Gambino

In this paper we study the Degn–Harrison system with a generalized reaction term. Once proved the global existence and boundedness of a unique solution, we address the asymptotic behavior of the system. The conditions for the global asymptotic stability of the steady state solution are derived using the appropriate techniques based on the eigen-analysis, the Poincaré–Bendixson theorem and the direct Lyapunov method. Numerical simulations are also shown to corroborate the asymptotic stability predictions.

Moreover, we determine the constraints on the size of the reactor and the diffusion coefficient such that the system does not admit non-constant positive steady state solutions.



中文翻译:

广义Degn-Harrison反应扩散系统:渐近稳定性和不存在结果

在本文中,我们研究了带有广义反应项的Degn–Harrison系统。一旦证明了唯一解的全局存在性和有界性,我们就可以解决系统的渐近行为。基于特征分析,庞加莱-本迪克森定理和直接Lyapunov方法,使用适当的技术来推导稳态解的全局渐近稳定性的条件。还显示了数值模拟,以证实渐近稳定性的预测。

此外,我们确定了对反应堆尺寸和扩散系数的约束,以使系统不接受非恒定的正稳态解。

更新日期:2020-07-16
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