The Enskog-Boltzmann equation in the whole space \({\mathbb{R}}^ 3:\) Some global existence, uniqueness and stability results (Q1096092)

The Enskog-Boltzmann equation, a partial differential integral equation of the hyperbolic type, is a model which generalizes the classical Boltzmann equation to high gas densities and is here considered with an analysis of the well-posedness of the initial-value problem in unbounded domains. Some new global existence and uniqueness results for the solutions of the initial-value problem and a discussion on the asymptotic stability are provided under suitable assumptions about the size of the norm of the initial data and about the rate of decay to zero at infinity in the phase space.