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SUMMARY:On hyperbolic approximations for a class of dispersive and diffusi
 ve-dispersive equations
DTSTART:20260407T091500Z
DTEND:20260407T101500Z
DTSTAMP:20260412T085800Z
UID:indico-event-16190@indico.math.cnrs.fr
DESCRIPTION:Speakers: Firas Dhaouadi\n\nWe introduce new approximate syste
 ms for dispersive and diffusive-dispersive equations with nonlinear fluxes
 . For purely dispersive equations\, we construct a  first-order\, strictl
 y hyperbolic approximation. Local well-posedness of smooth solutions is ac
 hieved by constructing a unique symmetrizer that applies to arbitrary smoo
 th fluxes. Under stronger conditions on the fluxes\, we provide a strictly
  convex entropy for the hyperbolic system that corresponds to the energy o
 f the underlying dispersive equation.To approximate diffusive-dispersive e
 quations\, we rely on a viscoelastic damped system that is compatible with
  the found entropy for the hyperbolic approximation of the dispersive evol
 ution. For the resulting hyperbolic-parabolic approximation\, we provide a
  global well-posedness result. The structure of the new approximate syste
 ms allows to apply standard numerical simulation methods from the field of
  hyperbolic balance laws. We confirm the convergence of our approximations
  even beyond the validity range of our theoretical findings on a set of te
 st cases covering different target equations. We show the applicability of
  the approach for strong nonlinear effects leading to oscillating or shock
 -layer-forming behavior. \n\nhttps://indico.math.cnrs.fr/event/16190/
URL:https://indico.math.cnrs.fr/event/16190/
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