On convergence of solutions of fractal burgers equation toward rarefaction waves

被引：43

作者：

Karch, Grzegorz ^{[1
]}

Miao, Changxing ^{[2
]}

Xu, Xiaojing ^{[3
]}

机构：

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

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

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

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 39卷 / 05期

关键词：

fractal Burgers equation; asymptotic behavior; rarefaction wave; Riemann problem; Levy process;

D O I：

10.1137/070681776

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the large time behavior of solutions of the Cauchy problem for the one-dimensional fractal Burgers equation u(t) +(-partial derivative(2)(x))(alpha/2) u + uu(x) = 0 with alpha = (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u +/- (u(-) < u(+)) as x -> +/-infinity, respectively, then the corresponding solution converges toward the rarefaction wave, i.e., the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.

引用

页码：1536 / 1549

页数：14

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