On the global existence and uniqueness of weak solutions to the nonstationary semiconductor equations

In this paper, we investigate the parabolic-elliptic coupled equation system, subject to mixed boundary conditions, describing the transport of the nonstationary carriers in a laser semiconductor device. The global existence of the weak solutions is proved under the condition that the initial values n(u) P-u is an element of L-2(Omega) (dim Omega less than or equal to 3). Moreover, the uniqueness of the weak solution is proved for dim Omega less than or equal to 2. (C) 2000 Elsevier Science Inc. All rights reserved.