Christopher Hermosilla, 9 h

Vincent Perrolaz, 10 h

Fabio Camilli, 11 h – Kolmogorov entropy of numerical solutions for scalar conservation lawswith convex <a href="http://flux.

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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 lawswith convex flux
Abstract:Following Lax’s information-theoretic perspective, we study thequantitative compactness of numerical solutions to scalar conservationlaws with uniformly convex flux via Kolmogorov entropy. We prove thatconservative and monotone finite-difference schemes satisfying adiscrete one-sided Lipschitz condition preserve the optimal continuousentropy scaling established by De Lellis–Golse and Ancona–Glass–Nguyen.The upper bound stems from the discrete Lipschitz structure, while thelower bound relies on a uniform approximation of BV functions. Thesefindings rigorously confirm the high-resolution nature of first-orderschemes in Lax’s sense. Finally, we formulate a general transferprinciple for the lower bound and discuss its applications toinformation recovery via numerical post-processing
 
 

https://indico.math.cnrs.fr/event/17080/