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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2014

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 $\varepsilon$ 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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Stéphane Junca. High frequency waves and the maximal smoothing effect for nonlinear scalar conservation laws. SIAM Journal on Mathematical Analysis, 2014, 46 (3), pp.2160-2184. ⟨10.1137/120880367⟩. ⟨hal-00576662v3⟩
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