Non-uniqueness of weak solutions for the fractal Burgers equation

被引：36

作者：

Alibaud, Nathael ^{[1
]}

Andreianov, Boris ^{[1
]}

机构：

[1] CNRS, UMR 6623, Lab Math Besancon, F-25030 Besancon, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2010年 / 27卷 / 04期

关键词：

Fractional Laplacian; Non-local diffusion; Conservation law; Levy-Khintchine's formula; Entropy solution; Admissibility of solutions; Oleinik's condition; Non-uniqueness of weak solutions; GLOBAL WELL-POSEDNESS; ASYMPTOTICS;

D O I：

10.1016/j.anihpc.2010.01.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The notion of Kruzhkov entropy solution was extended by the first author in 2007 to conservation laws with a fractional Laplacian diffusion term; this notion led to well-posedness for the Cauchy problem in the L-infinity-framework. In the present paper, we further motivate the introduction of entropy solutions, showing that in the case of fractional diffusion of order strictly less than one, uniqueness of a weak solution may fail. (C) 2010 Elsevier Masson SAS. All rights reserved.

引用

页码：997 / 1016

页数：20

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