Lower compactness estimates for scalar balance laws |
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| Authors: | Fabio Ancona Olivier Glass Khai T Nguyen |
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| Institution: | 1. Dipartimento di Matematica Pura, ed Applicata, Universita degli Studi di Padova Via Trieste 63 35121 Padova ITALY;2. Ceremade, Universite Paris‐Dauphine, CNRS UMR 7534, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE |
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| Abstract: | In this paper, we study the compactness in L of the semigroup (St)t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax. Upper estimates for the Kolmogorov e‐entropy of the image of bounded sets in L1 n L∞ through St were given by C. De Lellis and F. Golse. Here we provide lower estimates on this e‐entropy of the same order as the one established by De Lellis and Golse, thus showing that such an e‐entropy is of size ≈ 1/ε. Moreover, we extend these estimates of compactness to the case of convex balance laws. © 2012 Wiley Periodicals, Inc. |
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