Asymptotic expansion of solutions to the drift–diffusion equation with fractional dissipation

The initial-value problem for the drift–diffusion equation arising from the model of semiconductor device simulations is studied. The dissipation on this equation is given by the fractional Laplacian (−Δ)θ/2(−Δ)θ/2. Large-time behavior of solutions to the drift–diffusion equation with 0<θ≤10<θ≤1 is discussed. When θ>1θ>1, large-time behavior of solutions is known. However, when 0<θ≤10<θ≤1, the perturbation methods used in the preceding works would not work. In this paper, the asymptotic expansion of solutions with high-order is derived.