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SUMMARY:Dispersion and regularity for scalar conservation laws in several 
 space dimensions
DTSTART:20231208T141500
DTSTAMP:20260406T084353Z
UID:d983b684718ecef1c1c89d21c5069c86de22535414780fe3fc76076e
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Denis Serre (ENS Lyon)\nAbstract:\nThe analysis of scala
 r conservation laws is harder in several space dimensions\, than in one sp
 ace dimension\, because characteristic lines do not behave nicely. Functio
 nal analysis can be used because Kruzkhov's semi-group is $L^1$-contractin
 g. Crandall raised the question of whether the continuous extension of the
  semi-group to $L^1$\, or even to $L^1+L^\\infty$\, is meaningful: does it
  provide distributional solutions to the Cauchy problem ? With L. Silvestr
 e (Chicago)\, we solved this question by establishing dispersive propertie
 s: in presence of non-linearity\, the abstract solution becomes instaneous
 ly bounded in space\, the fluxes make sense and the PDE\, together with th
 e entropy differential inequalities\, are satisfied in the distributional 
 sense. Next\, we provide a non-trivial (in a sense that will be explained)
  estimate of Besov style\, of solutions up to the time of the first shock 
 formation.\nThese results are established by means of a functional analysi
 s tool that we developped recently\, called Compesnated Integrability.
LOCATION:MA B1 11 https://plan.epfl.ch/?room==MA%20B1%2011
STATUS:CONFIRMED
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