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A particle system approach to aggregation phenomena

Part of: Mathematical biology in general Physiological, cellular and medical topics Special processes Parabolic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  12 July 2019

Franco Flandoli  and
Marta Leocata
Franco Flandoli*
Affiliation:
Scuola Normale Superiore di Pisa
Marta Leocata*
Affiliation:
University of Pisa
*
*Postal address: Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, Pisa, Italy. Email address: [email protected]
**Postal address: Dipartimento di Matematica, University of Pisa, Largo Pontecorvo 5, Pisa, Italy. Email address: [email protected]
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Abstract

Inspired by a PDE–ODE system of aggregation developed in the biomathematical literature, we investigate an interacting particle system representing aggregation at the level of individuals. We prove that the empirical density of the individual converges to the solution of the PDE–ODE system.

Keywords

Aggregation phenomenapopulation dynamicmacroscopic limitparticle systemsemigroup approach

MSC classification

Primary: 35K57: Reaction-diffusion equations 35Q92: PDEs in connection with biology and other natural sciences 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 92B05: General biology and biomathematics 92C17: Cell movement (chemotaxis, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 282 - 306
Copyright
© Applied Probability Trust 2019 

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