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Asymptotic Analysis of Reaction-Diffusion systems

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In this talk, we shall address the general semilinear Reaction-Diffusion systems where the nonlinearity is present in the reaction term. These systems mathematically model the evolution of species concentration in a given medium under the influence of molecular diffusion and chemical reactions. The chemical reactions that we address are of reversible nature and the rate functions are always written using the law of mass action. Under diffuse scaling, we study the RD systems with oscillating diffusion coefficients and the perform the asymptotic analysis as the length-scale of heterogeneity tends to zero. In doing so, we derive a nonlinear homogenised diffusion model which depends on the chemical equilibrium of the reversible reaction. The homogenised model also turns out to be a cross-diffusion model in the spirit of Maxwell-Stefan system.

This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.

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