Space Homogeneous Solutions of the Linear Semiconductor Boltzmann Equation

The linear Boltzmann equation describing electron flow in a semiconductor is considered. The Cauchy problem for space-independent solutions is investigated, and without requiring a bounded collision frequency the existence of integrable solutions is established. Mass conservation, an H-theorem, and moment estimates also are obtained, assuming weak conditions. Finally, the uniqueness of the solution is demonstrated under a suitable hypothesis on the collision frequency.