The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. (English) Zbl 0963.60093

Stevens, Angela

SIAM J. Appl. Math. 61, No. 1, 183-212 (2000); erratum ibid. 61, No. 6, 2200 (2001).

Summary: The chemotaxis equations are a well-known system of partial differential equations describing aggregation phenomena in biology. Here they are rigorously derived from an interacting stochastic many-particle system, where the interaction between the particles is rescaled in a moderate way as population size tends to infinity. The novelty of this result is that in all previous applications of this kind of limiting procedure, the principal part of the system is assumed to fulfill an ellipticity condition which is not satisfied in our case. New techniques which deal with this difficulty are presented.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
35K55	Nonlinear parabolic equations
60J60	Diffusion processes
35Q80	Applications of PDE in areas other than physics (MSC2000)
92B05	General biology and biomathematics

Keywords:

aggregation; chemotaxis; limit dynamics; moderate interaction; stochastic many-particle system