On a drift-diffusion system for semiconductor devices
  In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two and three dimensions. We also provide the first term of the asymptotic expansion as $t\rightarrow\infty$. 
Rafael Granero-Belinch\'on
math.AP