Abstract
We shall consider the large number asymptotics of particle models for partial differential equations describing two component mixtures with simplest kind of self-consistent couplings. We shall recall in particular two examples related to different classes of models, the first one having both particle-like components and the second one having only one particle-like component (the other being described as a fluid); for these examples, different techniques on the probabilistic and analytic point of view are to be used to rigorously prove the convergence to a limit of the self-consistent terms in a “mean-field”-like asymptotics. The two models were analysed resp. in Bernardin and Ricci (Kinet Relat Models 4(3), 633–668, 2011) and Desvillettes et al. (Derivation of a homogenized two-temperature model from the heat equation. Preprint hal–00827912, arXiv:1305.6920, 2013, to be published in Mathematical Modelling and Numerical Analysis).
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References
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Ricci, V. (2014). Large Number Asymptotics for Two-Component Systems with Self-Consistent Coupling. In: Bernardin, C., Gonçalves, P. (eds) From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54271-8_14
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DOI: https://doi.org/10.1007/978-3-642-54271-8_14
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