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An existence and uniqueness theorem to the Cauchy problem for thermostatted-KTAP models. (English) Zbl 1250.35174
Summary: This paper is concerned with an integro-differential equation referred to as the thermostatted kinetic theory for active particles framework, which models complex systems under the action of an external force field, and constrained to kept constant the total energy (activity). The global in time existence and uniqueness of the solution to the relative Cauchy problem are proved for which the density and the activation energy moments of the solution are preserved.

MSC:
35R09Integro-partial differential equations
35A01Existence problems for PDE: global existence, local existence, non-existence
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness
35Q91PDEs in connection with game theory, economics, social and behavioral sciences
35Q92PDEs in connection with biology and other natural sciences
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