ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35Q60, 35B40, 35B25, 35L45 Jochmann, Frank, Institut fuer Angewandte Mathematik II, HU-Berlin, Unter den Linden 6, 10099 Berlin, Germany Existence and asymptotic behavior of weak solutions of the drift diffusion equations for semiconductors Global existence of solutions to the transient drift-diffusion equations coupled with Maxwell’s equations, which describe the charge transport in semiconductors, is shown. Uniqueness of solutions in the two-dimensional case follows from H^{s} and L^{p}- regularity results. Here a H^{1+s}-regularity result for elliptic equations with mixed boundary conditions is used. Furthermore, is shown under a suitable smallness assumption that the solutions converge for t → ∞ to stationary states. References: W. Fang, K. Ito, J. Diff. Eq., 117, (1995), 245-280. F. Jochmann, J. Math. Anal. Appl.204, (1996), 655-676. F. Jochmann, Uniqueness and regularity for the two-dimensional DDM for semiconductors coupled with ME, to appear in J. Diff. Equ. F. Jochmann, Appl. Anal. vol. 66, pp. 189-203.