Upper bound on heat kernels of finite particle systems of Keller-Segel type

2025/08/14 by Boutiah, S. E., Kinzebulatov, D.
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.10892

Abstract

We obtain an upper bound on the heat kernel of the Keller-Segel finite particle system that exhibits blow up effects. The proof exploits a connection between Keller-Segel finite particles and certain non-local operators. The latter allows to address some aspects of the critical behaviour of the Keller-Segel system resulting from its two-dimensionality.

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• Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up
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• Particle approximation of the doubly parabolic Keller-Segel equation in the plane
• Blow-up prevention by sub-logistic sources in 2d Keller-Segel system