A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: the one-dimensional case

DOI10.3150/19-BEJ1158zbMath1470.92043arXiv1712.10254MaRDI QIDQ2295035

Milica Tomašević, Denis Talay

Publication date: 12 February 2020

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.10254

zbMATH Keywords

chemotaxisKeller-Segel systemglobal-in-time solutionsMcKean-Vlasov-Fokker-Planck equation

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Cell movement (chemotaxis, etc.) (92C17)

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 ⋮ Stochastic model of chemotaxis in system of two populations ⋮ Mean field limit and quantitative estimates with singular attractive kernels ⋮ Probabilistic interpretation of the Cauchy problem for systems of nonlinear parabolic equations ⋮ Stochastic models of chemotaxis processes ⋮ A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: the two-dimensional case ⋮ McKean-Vlasov type stochastic differential equations arising from the random vortex method ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications

Cites Work

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• The one-dimensional chemotaxis model: global existence and asymptotic profile
• The 2-D stochastic Keller-Segel particle model : existence and uniqueness

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