Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility

2022/09/22 by Sara Daneri, Daneri, Sara, Emanuela Radici +3 · 2 citations
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2209.10884

openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong L¹-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any bounded initial data of finite energy. In order to prove well-posedness and convergence of the scheme with no BV or no vacuum assumptions and overcome the issues posed in this setting by the presence of a mobility function, we improve and strengthen the techniques introduced in arXiv:2012.01966(2).

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