Matinée de contrôle optimal
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Christopher Hermosilla, 9 h
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Vincent Perrolaz, 10 h
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Fabio Camilli, 11 h - Kolmogorov entropy of numerical solutions for scalar conservation laws
with convex flux.
Chaque séminaire durera 45 minutes, suivies de 15 minutes de questions et de pause-café.
Fabio Camilli:
Kolmogorov entropy of numerical solutions for scalar conservation laws
with convex flux.
Abstract:
Following Lax’s information-theoretic perspective, we study the
quantitative compactness of numerical solutions to scalar conservation
laws with uniformly convex flux via Kolmogorov entropy. We prove that
conservative and monotone finite-difference schemes satisfying a
discrete one-sided Lipschitz condition preserve the optimal continuous
entropy scaling established by De Lellis–Golse and Ancona–Glass–Nguyen.
The upper bound stems from the discrete Lipschitz structure, while the
lower bound relies on a uniform approximation of BV functions. These
findings rigorously confirm the high-resolution nature of first-order
schemes in Lax’s sense. Finally, we formulate a general transfer
principle for the lower bound and discuss its applications to
information recovery via numerical post-processing.