The initial-value problem for the drift-diffusion equation arising from themodel of semiconductor device simulations is studied. The dissipation on thisequation is given by the fractional Laplacian. When the exponent of thefractional Laplacian is large, large-time behavior of solutions is known.However, when the exponent is small, the perturbation methods used in thepreceding works would not work. Large-time behavior of solutions to thedrift-diffusion equation with small exponent is discussed. Particularly, theasymptotic expansion of solutions with high-order is derived.
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