In this paper we give a proof of the existence and uniqueness of smooth solutions for the nonlinear semiconductor Boltzmann equation. The method used allows to obtain global existence in time and uniqueness for dimensions 1 and 2. For dimension 3 we only can assure local existence in time and uniqueness. First, we define a sequence of solutions for a linearized equation and then, we prove the strong convergence of the sequence in a suitable space. The method relies in the use of interpolation estimates in order to control the decay of the solution when the wave vector goes to infinity.
Cite this article
Jean-Claude Guillot, Global Existence of Solutions for the Nonlinear Boltzmann Equation of Semiconductor Physics. Rev. Mat. Iberoam. 6 (1990), no. 1, pp. 43–59