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Séminaire du LJLL - 22 02 2019 14h00 : J.J. López Velázquez
Juan José López Velázquez (Université de Bonn)
On the growth of a particle coalescing in a Poisson distribution of obstacles
Résumé
A classical problem in mathematical physics is the derivation of kinetic equations taking as starting point the dynamics of its individual components. There are currently several rigorous results in this direction for particles whose dynamics is given by a Hamiltonian system. Another example of kinetic equation is the so-called Smoluchowski equation which describes the distribution of sizes of a system of particles which evolve according to some deterministic or stochastic dynamics and merge when they collide. In this talk I will discuss the rigorous derivation of the kinetic equation which describes the growth of a moving particle which coalesces with a set of scatterers. The well-posedness and the long time asymptotics of the resulting equation will be also discussed.