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

被引:6
|
作者
Yamamoto, Masakazu [1 ]
Sugiyama, Yuusuke [2 ]
机构
[1] Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan
[2] Tokyo Univ Sci, Dept Math, Tokyo 1628601, Japan
关键词
Drift-diffusion equation; Fractional dissipation; Large-time behavior; LARGE-TIME BEHAVIOR; GLOBAL WELL-POSEDNESS; PARABOLIC-SYSTEM; MAXIMUM PRINCIPLE; CHEMOTAXIS; EXISTENCE; DECAY; MODEL;
D O I
10.1016/j.na.2016.03.021
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 (-Delta)(theta/2). Large-time behavior of solutions to the drift-diffusion equation with 0 < theta <= 1 is discussed. When theta > 1, large-time behavior of solutions is known. However, when 0 < theta <= 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. (C) 2016 Elsevier Ltd. All rights reserved.
引用
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页码:57 / 87
页数:31
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