From microscopic to macroscopic descriptions of complex systems

Comptes Rendus - Mecanique

Volumn 331, Issue 11, 2003, Pages 733-738

  Lachowicz, Mirosław ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Complex systems; Continuum mechanics; ODE; Reaction diffusion equations; Stochastic semigroups

Indexed keywords

STOCHASTIC METHOD;

ARTICLE; DIFFUSION; MATHEMATICAL ANALYSIS; MECHANICS; MICROSCOPY; PROBABILITY; REACTION ANALYSIS; STOCHASTIC MODEL;

EID: 0242510816     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2003.09.003     Document Type: Article

References (12)

1. R. O'Malley Jr., Singular Perturbation Methods for ODE, Springer, New York, 1991.
2. M. Lachowicz, On bilinear kinetic equations. Between micro and macro description of biological populations, Banach Center Publ., in press.
3. A. Lasota, M.C. Mackey, Chaos, Fractals, and Noise, Springer, New York, 1994.
4. M. Lachowicz, D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci. 11 (2001) 1375-1390.
5. L. Arlotti, N. Bellomo, Population dynamics with stochastic interaction, Transport Theory Statist. Phys. 24 (1995) 431-443.
6. L. Arlotti, N. Bellomo, E. De Angelis, Generalized kinetic Boltzmann models: Mathematical structures and applications, Math. Models Methods Appl. Sci. 12 (2002) 571-596.
7. L. Arlotti, N. Bellomo, M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Phys. 29 (2000) 125-139.
8. E. Jäger, L. Segel, On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math. 52 (1992) 1442-1468.
9. M. Lachowicz, From microscopic to macroscopic description for generalized kinetic models, Math. Models Methods Appl. Sci. 12 (2002) 985-1005.
10. M. Lachowicz, M. Pulvirenti, A stochastic particle system modeling the Euler equation, Arch. Rational Mech. Anal. 109 (1990) 81-93.
11. M. Lachowicz, General population systems. Macroscopic limit of a class of stochastic semigroups, in press.
12. M. Lachowicz, Describing competitive systems at the level of interacting individuals, in: Proceedings of the Eight National Conference on Applications of Mathematics in Biology and Medicine, Łajs, 25-28 September, 2002, pp. 95-100.