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Kinetic equations and Markov jump processes

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Partial Differential Equations in Kinetic Theories

The first part of the talk is an introduction. The Boltzmann equation, Smoluchowski’s coagulation equation and the multiple fragmentation equation are considered and related stochastic particle models are introduced. In the second part of the talk, a particular phase transition in fragmentation models is studied. This transition is related to the formation of infinitely small particles. It corresponds to the existence of non-conservative solutions of the kinetic equation and to explosion (fast accumulation of jumps) in the stochastic model.

This talk is part of the Isaac Newton Institute Seminar Series series.

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