On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Tom 63 / 2003

Miros/law Lachowicz Banach Center Publications 63 (2003), 217-230 MSC: 35K45, 45K05, 82A40, 92D25, 76P05 DOI: 10.4064/bc63-0-10


In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the “microscopic level”). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the “macroscopic level”) including the “SIR” model, some competitive systems and the Smoluchowski coagulation model.


  • Miros/law LachowiczInstitute of Applied Mathematics and Mechanics
    Faculty of Mathematics, Informatics and Mechanics
    Warsaw University
    Banacha 2, 02-097 Warszawa, Poland

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