Convergence of a linearly transformed particle method for aggregation\n equations

2015/07/27 by Martin Campos Pinto, Pinto, Martin Campos, José A. Carrillo +5 · 1 citation
Immunology and Microbiology · Medicine · #Bone and Joint Diseases #FOS: Mathematics #Immune cells in cancer #Mathematical and Theoretical Epidemiology and Ecology Models #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1507.07405

openalex publication_date 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a linearly transformed particle method for the aggregation equation\nwith smooth or singular interaction forces. For the smooth interaction forces,\nwe provide convergence estimates in L¹ and L^\∞ norms depending on the\nregularity of the initial data. Moreover, we give convergence estimates in\nbounded Lipschitz distance for measure valued solutions. For singular\ninteraction forces, we establish the convergence of the error between the\napproximated and exact flows up to the existence time of the solutions in L¹\n\∩ L^p norm.\n

Cited by

• Convergence analysis of upwind type schemes for the aggregation equation\n with pointy potential

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