Mathematical analysis of a nonconservative discrete kinetic theory framework with thermostat
The mathematical modeling of complex biological systems requires the attention to nonconservative interactions which can modify the number of components. This paper deals with the definition and mathematical analysis of a Cauchy problem based on a new mathematical framework of the thermostatted kinetic theory. Specifically in order to take into account the role of the nonconservative interactions, a new thermostat operator is derived by imposing the conservation of a generic-order moment of the distribution function. The existence and uniqueness of the solution of the related Cauchy problem is proved by employing Lipschitz continuity arguments. Applications and future research directions are also discussed into the paper.