Extended Global Asymptotic Stability Conditions for a Generalized Reaction–Diffusion System

被引：0
作者：
Salem Abdelmalek
Samir Bendoukha
Belgacem Rebiai
Mokhtar Kirane
机构：
[1] Tebessa University,Mathematics and Computer Science Department
[2] Taibah University,Department of Electrical Engineering, College of Engineering
[3] Université de La Rochelle,LaSIE, Faculté des Sciences, Pole Sciences et Technologies
[4] King Abdulaziz University,NAAM Research Group, Department of Mathematics, Faculty of Science
[5] RUDN University,undefined
来源：
Acta Applicandae Mathematicae | 2019年 / 160卷
关键词：
Reaction diffusion equations; Lengyel–Epstein system; Global existence; Global asymptotic stability; 35K50; 35K57; 92D25;
D O I：
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摘要：
In this paper, we consider the general reaction–diffusion system proposed in Abdelmalek and Bendoukha (Nonlinear Anal., Real World Appl. 35:397–413, 2017) as a generalization of the original Lengyel–Epstein model developed for the revolutionary Turing-type CIMA reaction. We establish sufficient conditions for the global existence of solutions. We also follow the footsteps of Lisena (Appl. Math. Comput. 249:67–75, 2014) and other similar studies to extend previous results regarding the local and global asymptotic stability of the system. In the local PDE sense, more relaxed conditions are achieved compared to Abdelmalek and Bendoukha (Nonlinear Anal., Real World Appl. 35:397–413, 2017). Also, new extended results are achieved for the global existence, which when applied to the Lengyel–Epstein system, provide weaker conditions than those of Lisena (Appl. Math. Comput. 249:67–75, 2014). Numerical examples are used to affirm the findings and benchmark them against previous results.
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页数：19
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