The global existence of solutions and asymptotic stability of a reaction-diffusion system
Salem Abdelmalek, Samir Bendoukha, Mokhtar Kirane
TL;DR
This paper establishes conditions for the global existence and asymptotic stability of solutions to a generalized reaction-diffusion system, extending classical models and confirming results with numerical examples.
Contribution
It provides new sufficient conditions for stability in a generalized reaction-diffusion system with nonlinearities extending classical models.
Findings
Conditions for global asymptotic stability derived
Numerical examples confirm theoretical results
Generalization of classical reaction-diffusion models
Abstract
This paper studies the solutions of a reaction--diffusion system with nonlinearities that generalise the Lengyel--Epstein and FitzHugh--Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the system's solutions and confirmed through numerical Examples.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Mathematical and Theoretical Epidemiology and Ecology Models · Mathematical Biology Tumor Growth