"Reaction-diffusion systems derived from reactive Boltzmann equations"Bisi, MarziaWe present the derivation of proper reaction-diffusion equations for the number densities of the constituents of a reactive gas mixture, starting from suitably rescaled kinetic Boltzmann equations. We consider a binary mixture composed by a polyatomic (diatomic) and a monatomic gas diffusing in a gaseous background (typically, the atmosphere), and undergoing reversible and irreversible chemical reactions. The dominant process is assumed to be the elastic scattering with the host medium, while we propose two different scalings for the various chemical reactions: the first option leads to a system of three reaction-diffusion equations, while the second regime leads to two reaction-diffusion equations similar to the classical Brusselator system. Then, we study the Turing instability properties of such macroscopic systems, showing their dependence on particle masses, on collision frequencies of the Boltzmann operators, and, above all, on particle internal energies. This is a joint work with Romina Travaglini (University of Parma). |
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