Deterministic particle approximation of aggregation-diffusion equations on unbounded domains

2020/12/03 by Daneri, Sara, Radici, Emanuela, Runa, Eris · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.01966

Abstract

We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations with piecewise constant densities introduced in~\citeDi Francesco-Rosini starting from general bounded initial densities converge strongly in L¹ to bounded weak solutions of the PDE. In particular, the result is achieved in unbounded domains and for arbitrary nonnegative bounded initial densities, thus extending the results in \citeGosse-Toscani, Matthes-Osberger, Mathes-Soellner (in which a no-vacuum condition is required) and giving an alternative approach to \citeCarrillo-Craig-Patacchini in the one-dimensional case, including also subquadratic and superquadratic diffusions.

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• Guaranteeing Higher Order Convergence Rates for Accelerated Wasserstein Gradient Flow Schemes
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