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WELL-POSEDNESS OF DIFFUSION-AGGREGATION EQUATIONS WITH BOUNDED KERNELS AND THEIR MEAN-FIELD APPROXIMATIONS
  • LI CHEN,
  • PAUL NIKOLAEV,
  • David Prömel
LI CHEN
Universitat Mannheim

Corresponding Author:chen@uni-mannheim.de

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PAUL NIKOLAEV
Universitat Mannheim
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David Prömel
Universitat Mannheim
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Abstract

The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence argument to treat the non-linearity as well as a Moser iteration. Moreover, we prove a quantitative estimate in probability with arbitrary algebraic rate between the approximative interacting particle systems and the approximative McKean--Vlasov SDEs, which implies propagation of chaos for the interacting particle systems.
27 Oct 2023Submitted to Mathematical Methods in the Applied Sciences
30 Oct 2023Submission Checks Completed
30 Oct 2023Assigned to Editor
03 Nov 2023Review(s) Completed, Editorial Evaluation Pending
04 Nov 2023Reviewer(s) Assigned
02 Feb 2024Editorial Decision: Revise Minor
13 Feb 20241st Revision Received
13 Feb 2024Submission Checks Completed
13 Feb 2024Assigned to Editor
14 Feb 2024Reviewer(s) Assigned
21 Feb 2024Review(s) Completed, Editorial Evaluation Pending
08 Mar 2024Editorial Decision: Accept