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arXiv · 0907.3695

Non-uniqueness of weak solutions for the fractal Burgers equation

Nathael Alibaud·Boris Andreïanov
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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 $L^\infty$-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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Nathael Alibaud, Boris Andreïanov. 2009-09-09. Non-uniqueness of weak solutions for the fractal Burgers equation. https://doi.org/10.1016/j.anihpc.2010.01.008

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