Stationary states for the Kac equation with a Gaussian thermostat

Journal article, 2004

We study the stationary Kac equation in the presence of an external force field and a Gaussian thermostat and investigate the behaviour of a solution to this equation for varying field strength. We prove that for a weak field, the stationary density is continuous, but for a strong field the density has a singularity. Monte Carlo simulations illustrating the same are also presented.