Kinetic equations modelling population dynamics

被引：39

作者：

Arlotti, L ^{[1
]}

Bellomo, N

Lachowicz, M

机构：

[1] Univ Udine, Dept Mech, I-33100 Udine, Italy

[2] Politecn Torino, Dept Math, I-10128 Turin, Italy

[3] Univ Warsaw, Dept Math, Warsaw, Poland

来源：

TRANSPORT THEORY AND STATISTICAL PHYSICS | 2000年 / 29卷 / 1-2期

关键词：

population dynamics; kinetic models; generalized Boltzmann equation; Cauchy problem;

D O I：

10.1080/00411450008205864

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the analysis of a class of models of population dynamics with competition and kinetic interactions. Several models are proposed to describe the dynamics of large populations of individuals undergoing kinetic (stochastic) interactions which modify the states of the interacting pair. Models are characterized by time and space structure, and are motivated by recent research activity in mathematical immunology. The evolution equations are stated in terms of nonlinear integrodifferential equations which are similar to the Boltzmann equation. This paper deals with modelling and qualitative analysis of the related Cauchy problem.

引用

页码：125 / 139

页数：15

共 32 条

[1]

Adam J., 1996, SURVEY MODELS TUMOR

[2] BIASED RANDOM-WALK MODELS FOR CHEMOTAXIS AND RELATED DIFFUSION APPROXIMATIONS [J].

ALT, W .

JOURNAL OF MATHEMATICAL BIOLOGY, 1980, 9 (02) :147-177

[3] DUAL SEMIGROUPS AND 2ND ORDER LINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS [J].

AMANN, H .

ISRAEL JOURNAL OF MATHEMATICS, 1983, 45 (2-3) :225-254

[4]

[Anonymous], LECT NOTES MATH THEO

[5]

ARKERYD L, 1972, ARCH RATION MECH AN, V45, P1

[6] Qualitative analysis of a nonlinear integrodifferential equation modeling tumor-host dynamics [J].

Arlotti, L ;

Lachowicz, M .

MATHEMATICAL AND COMPUTER MODELLING, 1996, 23 (06) :11-29

[7]

Arlotti L., 1995, Transport Theory and Statistical Physics, V24, P431, DOI 10.1080/00411459508205138

[8]

Arlotti L., 1995, LECT NOTES MATH THEO

[9] Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods [J].

Bellomo, N .

MATHEMATICAL AND COMPUTER MODELLING, 1997, 26 (04) :13-34

[10] Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions [J].

Bellomo, N ;

De Angelis, E .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1998, 8 (08) :1403-1429

← 1 2 3 4 →