Generalized Kinetic (Boltzmann) Models: Mathematical Structures and Applications

Abstract

This paper deals with the development of suitable general mathematical structures including a large variety of Boltzmann type models. The contents are organized in three parts. The first part is devoted to modeling the above general framework. The second part to the development of specific models of interest in applied sciences. The third part develops a critical analysis towards research perspectives both on modeling and analytic problems.

Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

“…Additional bibliography can be recovered in the review papers by Bellomo and De Angelis (1998) and, more recently by Bellomo et al (2003a). Mathematical aspects related to the derivation and qualitative analysis of the above models can be recovered in Arlotti et al (2002b;. Additional studies are in progress as documented in .…”

On a mathematical model of immune competition

“…The analysis refers to class of models proposed in [1]-further developed in [2]-which consists of a system of nonlinear integro-differential equations with quadratic type nonlinearity. The structure is somewhat similar to that of classical models of the mathematical kinetic theory [3]. The above model was first proposed to describe the competition between tumor and immune cells, and then developed to model relatively general phenomena of the immune competition.…”

Modelling opinion formation by means of kinetic equations

“…If the collision process inside each group is standard, Lo Schiavo also defines another interaction process between individuals with different states and groups. Like in [2], the kinetic system that rises from these assumptions reads, for any…”