Uniform $H^{1,1}$-estimates for solutions of the stationary semiconductor device equations in one space dimension

Weiss, Jan-Philipp

facul_01; 27

Date: 24. 10. 2001
Abstract:
The stationary semiconductor device equations depend on a small
parameter $\lambda$ that corresponds to the so-called scaled Debye length.
Due to the influence of this small parameter, the system of equations
is singularly perturbed. Its solutions show a typical layer behaviour. This
work shows that the solutions are bounded independently of $\lambda$ in the
Sobolev space $H^{1,1}$ in the one-dimensional case. With help of this result,
one can prove uniform convergence for the Scharfetter-Gummel discretization
of the current equations. Our result completes the work of Gartland.

Primary MSC: 35J60 Nonlinear PDE of elliptic type
Secondary MSC: 34C11 Growth, boundedness, comparison of solutions, 34D15 Singular perturbations
Keywords: semiconductor device equations, singular perturbations, uniform convergence