Mathematical analysis of a nonconservative discrete kinetic theory framework with thermostat

  • Carlo Bianca Laboratoire Quartz EA 7393, \'{E}cole Sup\'{e}rieure d'Ing\'{e}nieurs en G\'{e}nie \'{E}lectrique,\\ Productique et Management Industriel, 95092 Cergy-Pontoise, France
  • Marco Menale Universit\`{a} degli Studi della Campania ``L. Vanvitelli", Viale Lincoln 5, I- 81100 Caserta, Italy


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.