Séminaire Orléans
On a probabilistic interpretation of the parabolic-parabolic Keller Segel equationsMilica Tomasevic (Ecole Polytechnique)
Thursday 28 January 2021 14:00 - Orléans - Salle de Séminaires
Résumé :
The Keller Segel model for chemotaxis is a two-dimensional system of parabolic or elliptic PDEs. Its particularity is that the solutions may blow-up in finite time. Motivated by the study of the fully parabolic model using probabilistic methods, we give rise to a non linear stochastic differential equation of McKean-Vlasov type with a highly non standard and singular interaction. Indeed, the drift of the equation involves all the past of one dimensional time marginal distributions of the process in a singular way. In terms of approximations by particle systems, an interesting and challenging difficulty arises: at each time each particle interacts with all the past of the other ones by means of a highly singular space-time kernel.
In this talk, after reviewing the literature about the Keller-Segel model, we will derive the above probabilistic interpretation and do an overview of results obtained. Some numerical insights will also be presented.
In this talk, after reviewing the literature about the Keller-Segel model, we will derive the above probabilistic interpretation and do an overview of results obtained. Some numerical insights will also be presented.
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