Preprint 2009-048
Non-uniqueness of weak solutions for the fractal Burgers equation
Nathaël Alibaud and Boris Andreďanov
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.