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Pré-Publication, Document De Travail Année : 2011

High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws

Résumé

The article first studies the propagation of well prepared high frequency waves with small amplitude $\eps$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, Tadmor, (1994), about the maximal regularizing effect for nonlinear conservation laws. For this purpose, a new definition of nonlinear flux is stated and compared to classical definitions. Then it is proved that the smoothness expected in Sobolev spaces cannot be exceeded.
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Dates et versions

hal-00576662 , version 1 (15-03-2011)
hal-00576662 , version 2 (11-02-2013)
hal-00576662 , version 3 (21-06-2015)

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  • HAL Id : hal-00576662 , version 1

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Stéphane Junca. High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws. 2011. ⟨hal-00576662v1⟩
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