On the nonlinear Boltzmann equation of the carrier transport in semiconductors. I: Existence and uniqueness of solutions (Q1106424)

The existence and uniqueness of solutions are shown for a steady-state, spatially homogeneous nonlinear Boltzmann equation describing the charge carrier transport in semiconductors. In contrast to more known kinds of Boltzmann equation in radiation transport or in the kinetic gas theory, the considered form contains Dirac's \(\delta\)-functions in the kernel of the collision integral. Therefore, smooth functions are transformed by the collision operator into discontinuous ones in general. The precise investigation of the properties of the operators describing the Boltzmann equation leads to the construction of suitable anisotropic Sobolev spaces.