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Description

  • Christopher Hermosilla, 9 h

  • Vincent Perrolaz, 10 h

  • 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

Christopher Hermosilla:

On Hamilton-Jacobi Equations of Mechanical Type in the Wasserstein Space

Abstract: In this talk, we discuss the well-posedness of possibly unbounded viscosity solutions to time- dependent, first-order Hamilton-Jacobi equations with mechanical Hamiltonian defined on the quadratic Wasserstein space. This problem naturally arises as the limiting case of a family of perturbed problems, in which the associated Lagrangian is regularized by the gradient of a relative entropy functional. While well-posedness is well understood for the Hamilton Jacobi equation corresponding to the entropy-regularized (or perturbed) Lagrangian, it has remained an open question whether the same viscosity techniques can be applied to the limiting, unperturbed problem. The main contribution of this work is to show that this limiting case can be treated within essentially the same viscosity-solution framework as the perturbed case

Vincent Perrolaz:

Galois Connections in Hamilton - Jacobi Equations and Conservation Laws

Abstract: 

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