= Keller--Segel model
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= Keller--Segel system
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A Keller--Segel model couples the density of moving cells to a chemical field that biases their motion. A common cell conservation law is $b_t=Db_{xx}-\partial_x(\chi(c)b c_x)$. Chemical dynamics depend on the application: the attractant may be produced by cells, or a nutrient may instead be consumed. The nutrient-consumption model $c_t=-kb$ with no nutrient diffusion gives travelling bacterial bands rather than prescribing the chemical externally.
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