Classical solutions of van Roosbroeck's equations with discontinuous coefficients and mixed boundary conditions on two dimensional space domains
Van Roosbroeck's equations describe the motion of electrons and holes
in semiconductor devices.
The system of these equations admits a unique, local in time solution
in a space of functions over a two-dimensional spatial domain which
are absolutely integrable to some exponent p>1.
A large variety of recombination terms, including nonlocal ones, is
This theorem is derived from results in  about classical solutions
of quasilinear parabolic systems on two dimensional domains by
reformulating van Roosbroeck's system as a quasilinear parabolic
system for the electro-chemical potentials of electrons and holes.
This treatment of van Roosbroeck's system is consistent with a balance
principle formulation of the equations and allows to justify their
approximation using finite volume discretization schemes.
H.-Chr. Kaiser, H. Neidhardt, and J. Rehberg, Classical solutions of
quasilinear parabolic systems on two dimensional domains, Preprint
Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117
Berlin, Germany, 2002.