Global Approximate Newton Methods.
Global existence of solutions for the non linear Boltzmann equation of semiconductor physics.
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 can only 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 metod relies on the use of interpolation estimates...