Nonlinear diffusion of test particles in the presence of an external conservative force

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Abstract
The diffusion of certain test particles that in the presence of an external constant conservative force, undergo collisions against the field particles of an infinite homogeneous host medium as well as between themselves, is studied on the basis of an integral reformulation of the relevant stationary spatially-independent nonlinear integrodifferential Boltzmann equation. The existence and uniqueness of the solution for the distribution function of the test particles considered is investigated by an application of the contracting mapping principle for both the general nonlinear case and for the linearized one as resulting through an appropriate decomposition of the sought distribution function. Also, the case when the scattering probability is represented as a factorized expansion of finite rank is discussed in some detail.

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