A positivity-preserving numerical scheme for a nonlinear fourth order parabolic system

A positivity-preserving numerical scheme for a fourth order nonlinear parab olic system arising in quantum semiconductor modeling is studied. The syste m is numerically treated by introducing an additional nonlinear potential a nd a subsequent semidiscretization in time. The resulting sequence of nonli near second order elliptic systems admits at each time level strictly posit ive solutions, which is proved by an exponential transformation of variable s. The stability of the scheme is shown and convergence is proved in one sp ace dimension. Numerical results concerning the switching behavior of a res onant tunneling diode are presented.