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EnglishIn 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.
Abbad A., Abdelmalek S., Bendoukha S., & Gambino G. (2021). A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 57, 1-28 [10.1016/j.nonrwa.2020.103191].
| Data di pubblicazione: | 2021 | |
| Titolo: | A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results | |
| Autori: | GAMBINO, Gaetana (Corresponding) | |
| Citazione: | Abbad A., Abdelmalek S., Bendoukha S., & Gambino G. (2021). A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 57, 1-28 [10.1016/j.nonrwa.2020.103191]. | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.nonrwa.2020.103191 | |
| Abstract: | 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. | |
| Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| gambino_rg.pdf | Pre-print | Open Access Visualizza/Apri | ||
| 1-s2.0-S1468121820301097-main.pdf | Versione Editoriale | Administrator Richiedi una copia |
http://hdl.handle.net/10447/432004
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