Kinetic theory, particle systems and their hydrodynamic limits



This project deals with the derivation of hydrodynamic equations from a detailed description of matter, such as the kinetic theory or the particle systems theory. In the former, we consider a chemically reactive mixture described by a Boltzmann type model and investigate the reaction-diffusion limit corresponding to different evolution regimes for what concerns diffusion process and chemical reaction. From the laws governing the molecular interactions, we derive hydrodynamic equations, diffusion coefficients, and chemical production terms. In the latter, we consider random particle interactions and derive macroscopic equations as PDEs or stochastics PDEs for the conserved quantities. We focus on two types of models, ones with degenerate and non-gradient rates and others with longrange interactions and with reservoirs. The goal is to analyze the impact of changing locally the dynamics and see how it affects the macroscopic behavior.

Ref. FCT

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University of Lisboa
Association Léonard de Vinci
Paris École Polytechnique in Paris

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