Abstract
In this paper, we construct a weak solution to the unipolar quantum drift-diffusion model in a bounded domain with Neumann boundary conditions, thereby extending an existence result in Gianazza et al. (Arch Rational Mech Anal 194:133–220, 2009) to the case where the boundary of the domain is only Lipschitz. We also obtain the limit of the solution as the scaled Planck constant $$\varepsilon $$ in the problem goes to $$0$$ .
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