Collective motion driven by nutrient consumption

Pierre Emmanuel Jabin, Benoît Perthame

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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.

Original languageEnglish (US)
Pages (from-to)483-497
Number of pages15
JournalAsymptotic Analysis
Issue number4
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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