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The microscopic derivation and well-posedness of the stochastic Keller-Segel equation. (English) Zbl 1464.35363

A stochastic differential equation modelling diffusion-aggregation phenomena is studied. Cells (or particles) are also subject to individual (idiosyncratic) noises and common (environmental) noise. Well-posedness of that SDE generalizing the stochastic Keller-Segel system is studied, together with the mean-field limit.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35R60 PDEs with randomness, stochastic partial differential equations
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
60H30 Applications of stochastic analysis (to PDEs, etc.)
92C17 Cell movement (chemotaxis, etc.)
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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References:

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