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Kinetic Equations and Cell Motion: An Introduction

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Book cover The Dynamics of Biological Systems

Part of the book series: Mathematics of Planet Earth ((MPE,volume 4))

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Abstract

Kinetic theory is an old subject which finds its motivations in the description of fluids at the so-called mesoscopic scale where molecules interact but are too numerous for describing the interacting particles individually. We present several examples from physics, we give some mathematical background showing that the kinetic-transport equation enjoys interesting functional analytic properties as other partial differential equations. We also describe in full generality how macroscopic models are derived from kinetic equations. This material gives us the tools to introduce models for bacterial run and tumble motion. The subject has been progressing quickly in the last decades, and a hierarchy of models are now available up to the scale of molecular pathways describing the cell decision to tumble.

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Authors and Affiliations

  1. Sorbonne University, CNRS, Université de Paris, Laboratoire Jacques-Louis Lions, Paris, France

    Benoît Perthame

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  1. Benoît Perthame
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Correspondence to Benoît Perthame .

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Editors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Arianna Bianchi

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Thomas Hillen

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Mark A. Lewis

  4. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

    Yingfei Yi

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Perthame, B. (2019). Kinetic Equations and Cell Motion: An Introduction. In: Bianchi, A., Hillen, T., Lewis, M., Yi, Y. (eds) The Dynamics of Biological Systems. Mathematics of Planet Earth, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-22583-4_9

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