On the Cauchy problem for spatially homogeneous semiconductor Boltzmann equations: existence and uniqueness

The non-linear semi-classical Boltzmann equation for an electron gas in a semiconductor is investigated in the framework of Lebesgue spaces by first providing a rigorous definition of the collision operator. The case of possibly unbounded collision frequencies is treated. Global existence and uniqueness of integrable, space independent solutions to the related Cauchy problem are established. Entropy inequalities, upper bounds for moments as well as mass conservation are also obtained.