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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 141卷

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

页码：57 / 87

页数：31

共 50 条

[1] Asymptotic Behavior of Solutions to the Drift-Diffusion Equation with Critical Dissipation
Masakazu Yamamoto
Yuusuke Sugiyama
[J]. Annales Henri Poincaré, 2016, 17 : 1331 - 1352
[2] Asymptotic Behavior of Solutions to the Drift-Diffusion Equation with Critical Dissipation
Yamamoto, Masakazu
Sugiyama, Yuusuke
[J]. ANNALES HENRI POINCARE, 2016, 17 (06): : 1331 - 1352
[3] Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation
Sugiyama, Yuusuke
Yamamoto, Masakazu
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (02) : 1383 - 1417
[4] Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation
Yuusuke Sugiyama
Masakazu Yamamoto
[J]. Journal of Evolution Equations, 2021, 21 : 1383 - 1417
[5] Asymptotic expansion of solutions to the drift-diffusion equation with large initial data
Yamamoto, Masakazu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) : 144 - 163
[6] LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE DRIFT-DIFFUSION EQUATION WITH FRACTIONAL DISSIPATION
Yamamoto, Masakazu
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (7-8) : 731 - 758
[7] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION
Ogawa, Takayoshi
Yamamoto, Masakazu
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2009, 19 (06): : 939 - 967
[8] Existence and analyticity of solutions to the drift-diffusion equation with critical dissipation
Yamamoto, Masakazu
Kato, Keiichi
Sugiyama, Yuusuke
[J]. HIROSHIMA MATHEMATICAL JOURNAL, 2014, 44 (03) : 275 - 313
[9] Spatial analyticity of solutions to the drift-diffusion equation with generalized dissipation
Masakazu Yamamoto
[J]. Archiv der Mathematik, 2011, 97 : 261 - 270
[10] Spatial analyticity of solutions to the drift-diffusion equation with generalized dissipation
Yamamoto, Masakazu
[J]. ARCHIV DER MATHEMATIK, 2011, 97 (03) : 261 - 270

← 1 2 3 4 5 →