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SUMMARY:Kružkov’s doubling of variables: how far does it go?
DTSTART:20261021T080000Z
DTEND:20261021T100000Z
DTSTAMP:20261104T033000Z
UID:indico-event-17565@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicolas Masson (LMO)\n\nScalar conservation laws typ
 ically admit several weak solutions for the same initial datum. To single 
 out the physically relevant one\, the equation must be supplemented with a
  family of differential inequalities\, called the entropy inequalities. In
  his seminal 1970 paper\, Kružkov proved that entropy solutions are uniqu
 e: his argument relies on a one-parameter family of entropies\, |u-k|\, no
 w called Kružkov entropies. The key idea is to replace the constant k in 
 the entropy inequalities satisfied by one solution u_1 by a second entropy
  solution u_2 using a method known as doubling of variables. This yields t
 he Kato inequality\, from which it follows that ||u_1(t)-u_2(t)||_{L^1} is
  non-increasing in time\, and therefore uniqueness. Textbooks usually pres
 ent this proof under restrictive assumptions\, but Kružkov’s original a
 rgument covers a much more general setting: multi-dimensional equations\, 
 fluxes depending on (t\,x)\, and source terms. The goal of this talk will 
 be to present Kružkov’s proof\, identify the structural ingredients tha
 t make it work\, and discuss how and when the strategy can be extended to 
 other evolution equations\, as well as where it breaks down.\n\nhttps://in
 dico.math.cnrs.fr/event/17565/
URL:https://indico.math.cnrs.fr/event/17565/
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