Continuous model of opinion dynamics with convictions

In this note we study a new kinetic model of opinion dynamics. The incorporates two forces – alignment opinions under all-to-all communication driving the system to consensus, and Rayleigh type friction force that drives each 'player' its fixed conviction value. balance between these creates non-trivial limiting outcome.We establish existence global mono-opinion state, whereby any initial distribution for value aggregates Dirac measure concentrated on single opinion. We identify several cases where such state is unique depends continuously convictions. Several regularity properties are presented.