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

Abstract 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.

[1]  V. Liskevich,et al.  Gaussian bounds for propagators perturbed by potentials , 2006 .

[2]  N Bellomo,et al.  Complexity analysis and mathematical tools towards the modelling of living systems. , 2009, Physics of life reviews.

[3]  G. Ajmone Marsan,et al.  New paradigms towards the modelling of complex systems in behavioral economics , 2009, Math. Comput. Model..

[4]  A CONTINUOUS SIZE-STRUCTURED RED CORAL GROWTH MODEL , 2008 .

[5]  Adam C. McBride,et al.  Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation , 1998 .

[6]  Nicola Bellomo,et al.  On the foundations of cancer modelling: Selected topics, speculations, and perspectives , 2008 .

[7]  G. Ajmone Marsan.  On the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition , 2009, Comput. Math. Appl..

[8]  Juan Soler,et al.  MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS , 2010 .

[9]  N. Bellomo,et al.  Complexity and mathematical tools toward the modelling of multicellular growing systems , 2010, Math. Comput. Model..

[10]  Nicola Bellomo,et al.  From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications , 1999 .

[11]  Nicola Bellomo,et al.  Generalized kinetic (Boltzmann) models: mathematical structures and applications , 2002 .

[12]  Marcello Edoardo Delitala,et al.  MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES , 2009 .

[13]  Nicola Bellomo,et al.  On the complexity of multiple interactions with additional reasonings about Kate, Jules and Jim , 2008, Math. Comput. Model..

[14]  N. Bellomo,et al.  Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory. , 2008, Current topics in developmental biology.

[15]  Glenn F. Webb,et al.  Population Models Structured by Age, Size, and Spatial Position , 2008 .