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

• Autorzy: Mirosław Lachowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76P05: Rarefied gas flows, Boltzmann equation
• 45K05: Integro-partial differential equations
• 92D25: Population dynamics (general)
• 35K45: Initial value problems for second-order parabolic systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 63
• Numer: 1
• Strony: 217-230

Daty

wydano

2003

Twórcy

autor

Mirosław Lachowicz

• Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc63-0-10