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Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria

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  • In this paper we study the rate of convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. We first analyze a three-species system with boundary equilibria in some stoichiometric classes, and whose right hand side is bounded above by a quadratic nonlinearity in the positive orthant. We prove similar results on the convergence to the positive equilibrium for a fairly general two-species reversible reaction-diffusion network with boundary equilibria.

    Mathematics Subject Classification: 35B40, 35K57, 35Q92, 80A30, 80A32, 90E20.


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  • Figure 1.  Construction of a rectangular invariant region for the reversible reaction $ m_1A+n_1B\rightleftharpoons m_2A+n_2B $ for the cases a. $ \bar m = m_1-m_2, \ \bar n = n_2-n_1 $ nonzero and of the same sign; b. $ \bar m, \bar n $ nonzero and of different signs

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