Non-uniqueness of weak solutions for the fractal Burgers equation

Details Non-uniqueness of weak solutions for the fractal Burgers equation Non-uniqueness of weak solutions for the fractal Burgers equation

2009-07-21

arxiv.org/abs/0907.3695v3

Annales de l'Institut Henri Poincar\'e Analyse non lin\'eaire (2010) a paraitre

Mathematics

Analysis of PDEs

23 pages

Scientific paper

10.1016/j.anihpc.2010.01.008

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 $L^\infty$-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.

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