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Deterministic particle approximation of aggregation-diffusion equations

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FKTW02 - Frontiers in analysis of kinetic equations

We consider aggregation-diffusion equations on unbounded domains for arbitrary nonnegative and bounded initial densities. We show strong $L^1$ convergence of a deterministic particle scheme, in the one-dimensional setting. In particular, w.r.t. previous works, no BV bounds or lower bounds on the densities are required. We also discuss the flexibility of the approach and extensions to other settings and discuss some numerical simulations. This is a joint work with Emanuela Radici and Eris Runa.

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

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