Mean-field limit of a particle approximation of the one-dimensional parabolic-parabolic Keller-Segel model without smoothing

DOI10.1214/18-ECP183zbMath1402.60129arXiv1712.07490MaRDI QIDQ1994114

Milica Tomašević, Jean-François Jabir, Denis Talay

Publication date: 1 November 2018

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07490

zbMATH Keywords

interacting particle systemchemotaxis modelsingular McKean-Vlasov SDE

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Related Items (9)

Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel ⋮ Particle approximation of the doubly parabolic Keller-Segel equation in the plane ⋮ Propagation of chaos for stochastic particle systems with singular mean-field interaction of \(L^q - L^p\) type ⋮ Mean field limit and quantitative estimates with singular attractive kernels ⋮ Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions ⋮ A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: the two-dimensional case ⋮ A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: the one-dimensional case ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

Cites Work

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• Strong solutions of stochastic equations with singular time dependent drift
• Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic Keller-Segel system in the plane
• Convergence rate for the approximation of the limit law of weakly interacting particles: Application to the Burgers equation
• Schrödinger semigroups
• Convergence of a Stochastic Particle Approximation for Measure Solutions of the 2D Keller-Segel System
• The 2-D stochastic Keller-Segel particle model : existence and uniqueness

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