On the initial value problem of a class of models of the kinetic theory for active particles

被引：5

作者：

Arlotti, L. ^{[2
]}

De Angelis, E. ^{[1
]}

机构：

[1] Politecn Torino, Dipartimento Matemat, Turin, Italy

[2] Univ Udine, Dipartimento Ingn Civile, I-33100 Udine, Italy

来源：

APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 03期

关键词：

Kinetic theory; Cauchy problem; Evolution equations; SYSTEMS; COMPETITION; PARADIGMS; SIZE;

D O I：

10.1016/j.aml.2010.09.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the qualitative analysis of the Cauchy problem for a class of systems constituted by a large number of interacting entities called active particles. Their state includes, in addition to geometrical and mechanical variables, also a microscopic state related to their socio-biological behavior, which is called activity. Microscopic interactions are governed by the self-organizing ability, which finalizes the dynamics according to well defined strategies. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：257 / 263

页数：7

共 17 条

[1] From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications [J].

Arlotti, L ;

Bellomo, N ;

Latrach, K .

MATHEMATICAL AND COMPUTER MODELLING, 1999, 30 (1-2) :15-40

[2] Generalized kinetic (Boltzmann) models: Mathematical structures and applications [J].

Arlotti, L ;

Bellomo, N ;

De Angelis, E .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (04) :567-591

[3] Nonautonomous fragmentation equation via evolution semigroups [J].

Arlotti, L. ;

Banasiak, J. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (10) :1201-1210

[4] On the foundations of cancer modelling: Selected topics, speculations, and perspectives [J].

Bellomo, N. ;

Li, N. K. ;

Maini, P. K. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (04) :593-646

[5] Complexity and mathematical tools toward the modelling of multicellular growing systems [J].

Bellomo, N. ;

Bellouquid, A. ;

Nieto, J. ;

Soler, J. .

MATHEMATICAL AND COMPUTER MODELLING, 2010, 51 (5-6) :441-451

[6] Complexity analysis and mathematical tools towards the modelling of living systems [J].

Bellomo, N. ;

Bianca, C. ;

Delitala, M. .

PHYSICS OF LIFE REVIEWS, 2009, 6 (03) :144-175

[7] Complex multicellular systems and immune competition: New paradigms looking for a mathematical theory [J].

Bellomo, Nicola ;

Forni, Guido .

MULTISCALE MODELING OF DEVELOPMENTAL SYSTEMS, 2008, 81 :485-502

[8] On the complexity of multiple interactions with additional reasonings about Kate, Jules and Jim [J].

Bellomo, Nicola ;

Carbonaro, Bruno .

MATHEMATICAL AND COMPUTER MODELLING, 2008, 47 (1-2) :168-177

[9] MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS [J].

Bellomo, Nicola ;

Bellouquid, Abdelghani ;

Nieto, Juan ;

Soler, Juan .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2010, 20 (07) :1179-1207

[10] MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES [J].

De Lillo, S. ;

Delitala, M. ;

Salvatori, M. C. .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2009, 19 :1405-1425

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