Thermostatted Kinectic Theory Approach, The: Theory, Inverse Problems, and Models

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This monograph is devoted to the recently developed thermostatted kinetic theory and its application to the modeling of complex systems in a variety of fields. In the first part, the frameworks of the theory, which are obtained by coupling the kinetic theory for active particles with the thermostats coming from non-equilibrium statistical mechanics (Gaussian isokinetic thermostat), are presented. Among the theoretical results discussed are existence and uniqueness of the solution of the different mathematical frameworks, existence and uniqueness of the nonequilibrium stationary state, convergence to the nonequilibrium stationary state, derivation of macroscopic equations by asymptotic limits, and the construction of solutions to inverse problems based on the thermostatted kinetic theory. The second part deals with the derivation of mathematical models for nonequilibrium complex systems. Among those described within this new framework are immune systems and competition with tumors, keloid formation and therapy, dynamics of train crowds, modeling of a smart grid composed by different energy sources, and financial markets.