Non-uniqueness of weak solutions for the fractal Burgers equation |
| |
Authors: | Nathaë l Alibaud,Boris Andreianov |
| |
Affiliation: | Laboratoire de mathématiques de Besançon, UMR CNRS 6623, 16, route de Gray - 25 030 Besançon cedex, France |
| |
Abstract: | 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∞-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. |
| |
Keywords: | 35L65 35L67 35L82 35S10 35S30 |
本文献已被 ScienceDirect 等数据库收录! |
|