Global existence of weak solutions for a system of non‐linear Boltzmann equations in semiconductor physics

摘要

AbstractIn this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs aL2‐estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this pape