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SUMMARY:Matinée de contrôle optimal
DTSTART:20260918T070000Z
DTEND:20260918T100000Z
DTSTAMP:20260907T224000Z
UID:indico-event-17080@indico.math.cnrs.fr
DESCRIPTION:\n\nChristopher Hermosilla\, 9 h\n\n\nVincent Perrolaz\, 10 h\
 n\n\nFabio Camilli\, 11 h - Kolmogorov entropy of numerical solutions for 
 scalar conservation lawswith convex flux.\n\n\nChaque séminaire durera 45
  minutes\, suivies de 15 minutes de questions et de pause-café.\nChristop
 her Hermosilla:\nOn Hamilton-Jacobi Equations of Mechanical Type in the Wa
 sserstein Space\nAbstract: In this talk\, we discuss the well-posedness of
  possibly unbounded viscosity solutions to time- dependent\, first-order H
 amilton-Jacobi equations with mechanical Hamiltonian defined on the quadra
 tic 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-p
 osedness 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 vi
 scosity-solution framework as the perturbed case\nVincent Perrolaz:\nGaloi
 s Connections in Hamilton - Jacobi Equations and Conservation Laws\nAbstra
 ct: \nFabio Camilli: \nKolmogorov entropy of numerical solutions for scal
 ar conservation lawswith convex flux\nAbstract:Following Lax’s informati
 on-theoretic perspective\, we study thequantitative compactness of numeric
 al solutions to scalar conservationlaws with uniformly convex flux via Kol
 mogorov entropy. We prove thatconservative and monotone finite-difference 
 schemes satisfying adiscrete one-sided Lipschitz condition preserve the op
 timal continuousentropy scaling established by De Lellis–Golse and Ancon
 a–Glass–Nguyen.The upper bound stems from the discrete Lipschitz struc
 ture\, while thelower bound relies on a uniform approximation of BV functi
 ons. Thesefindings rigorously confirm the high-resolution nature of first-
 orderschemes in Lax’s sense. Finally\, we formulate a general transferpr
 inciple for the lower bound and discuss its applications toinformation rec
 overy via numerical post-processing\n \n \n\nhttps://indico.math.cnrs.fr
 /event/17080/
URL:https://indico.math.cnrs.fr/event/17080/
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