6533b7dcfe1ef96bd1272c6d
RESEARCH PRODUCT
A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results
Samir BendoukhaSalem AbdelmalekGaetana GambinoAbir Abbadsubject
Lyapunov functionSteady state (electronics)Asymptotic stability Existence of solutions Generalized Degn–Harrison system Non-constant steady state solutions Steady statesApplied Mathematics010102 general mathematicsGeneral EngineeringGeneral Medicine01 natural sciencesTerm (time)010101 applied mathematicsComputational Mathematicssymbols.namesakeExponential stabilityReaction–diffusion systemsymbolsApplied mathematics0101 mathematicsDiffusion (business)General Economics Econometrics and FinanceSettore MAT/07 - Fisica MatematicaAnalysisMathematicsdescription
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 Poincare–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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-02-01 |