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This paper deals with the introduction of nonconservative interactions in the thermostatted kinetic equations system, which is a set of autonomous partial integro-differential equations with quadratic nonlinearity. The time evolution of the solutions is obtained by considering three different operators: the operator which models conservative interactions, the operator that takes care of nonconservative interactions and the operator that allows the control of the moment evolution of the system. Applications refer to the modeling of complex biological and chemical systems. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a retarded partial integrodifferential equation that belongs to the class of thermostatted kinetic equations with time delay. Specifically, the paper is devoted to the proof of the existence and uniqueness of mild solutions of the related Cauchy problem. The main result is obtained by employing integration along the characteristic curves and successive approximations sequence arguments. Applications and perspective are also discussed within the paper. [ABSTRACT FROM AUTHOR]