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SUMMARY:Generalized Rankine -- Hugoniot relations for  shocks in dispersiv
 e media - Sergey Gavrilyuk (Aix Marseille Université)
DTSTART:20220713T103000Z
DTEND:20220713T110000Z
UID:TALK175868@talks.cam.ac.uk
DESCRIPTION:The Euler equations &nbsp\;of compressible fluids\, hyperelast
 icity\, MHD\, etc. are typical examples of hyperbolic systems of conservat
 ion laws admitting shock solutions\, i.e. discontinuous solutions satisfyi
 ng the governing equations in a weak sense. The corresponding equations of
  motion are the Euler-Lagrange equations for a functional which is the Ham
 ilton action. The dispersive regularizations of these models based on the 
 modification of the corresponding Lagrangian aim at avoiding discontinuiti
 es by replacing them by "dispersive shocks"\, i.e. by strongly oscillating
  non stationary fronts.&nbsp\;&nbsp\;&nbsp\;We show that in some cases dis
 persive regularization produces solutions that are "almost" classical shoc
 ks. &nbsp\;Such solutions must necessarily satisfy special &nbsp\;jump rel
 ations (generalized Rankine-Hugoniot relations) that follow naturally from
  the variational structure of the governing equations. &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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