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Journal Articles Asymptotic Analysis Year : 2022

Collective motion driven by nutrient consumption


A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary Differential Equation system which we scale so as to get a limit describing the usually observed pattern. In this limit the cell density is concentrated as a moving Dirac mass and the nutrient undergoes a discontinuity. We first carry out the analysis without diffusion, getting a complete description of the unique limit. When diffusion is included, we prove several specific a priori estimates and interpret the system as a heterogeneous monostable equation. This allow us to obtain a limiting problem which shows the concentration effect of the limiting dynamics.
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Dates and versions

hal-03766245 , version 1 (31-08-2022)


  • HAL Id : hal-03766245 , version 1


Pierre-Emmanuel Jabin, Benoît Perthame. Collective motion driven by nutrient consumption. Asymptotic Analysis, In press. ⟨hal-03766245⟩
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