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Pré-Publication, Document De Travail Année : 2011

Lower compactness estimates for scalar balance laws

Résumé

In this paper, we study the compactness in L^{1}_{loc} of the semigroup of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of this semi-group for each time t>0 was established by P. D. Lax. Upper estimates for the Kolmogorov's epsilon-entropy of the image through the semi-group of sets bounded in L^{1} and L^\infty were given by C. De Lellis and F. Golse. Here, we provide lower estimates on this epsilon-entropy of the same order. Moreover, we extend these estimates of compactness to the case of convex balance laws.

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Dates et versions

hal-00606311 , version 1 (06-07-2011)
hal-00606311 , version 2 (28-10-2011)

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  • HAL Id : hal-00606311 , version 1

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Fabio Ancona, Olivier Glass, Tien Khai Nguyen. Lower compactness estimates for scalar balance laws. 2011. ⟨hal-00606311v1⟩
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