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1 Dipartimento di Matematica Pura e Applicata Padova 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : 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.

Mots-clés : lois de conservation

Author: Fabio Ancona - Olivier Glass - Khai Tien Nguyen -

Source: https://hal.archives-ouvertes.fr/


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