Global solutions and \(L^ 1\)-stability to a nonlinear evolution problem in the diffusion of the particles of a mixture (Q1197188)

The paper deals with a particle transport problem in a mixture. The mixture consists of test particles, injected at \(t=0\) by a spatially uniform pulsed source, and of field particles. The test particles undergo binary collisions with the field particles or between themselves. The Boltzmann equation governing the system includes possible removal and the action of a time dependent external force. Global existence and uniqueness is proved in a suitably weighted normed space by means of a contraction argument. Stability of the solution with respect to \(L_ 1\) norm is also proved.