Two-dimensional fractal Burgers equation with step-like initial conditions

被引：6

作者：

Karch, Grzegorz ^{[1
]}

Pudelko, Anna ^{[2
]}

Xu, Xiaojing ^{[3
]}

机构：

[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland

[2] AGH Univ Sci & Technol, PL-30059 Krakow, Poland

[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 13期

关键词：

fractal Burgers equation; fractional Laplacian; rarefaction waves; self-similar solutions; VISCOUS CONSERVATION-LAWS; RAREFACTION WAVE; ASYMPTOTICS; STABILITY; DIFFUSION;

D O I：

10.1002/mma.3266

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the two-dimensional convection-diffusion equation with a fractional Laplacian, supplemented with step-like initial conditions. We show that the large time behavior of solutions to this IVP is described either by rarefaction waves, or diffusion waves, or suitable self-similar solutions, depending on the order of the fractional dissipation and on a direction of a convective nonlinearity. Copyright (c) 2014 John Wiley & Sons, Ltd.

引用

页码：2830 / 2839

页数：10

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