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Stabilite multidimensionnelle d'interfaces dynamiques. Application aux transitions de phase liquide-vapeur.

Abstract : We are interested in the stability of shock waves solutions to
multidimensional hyperbolic systems of conservation laws. This
problem was addressed by Andrew Majda under the so-called uniform
stability assumption. This assumption is crucial in Majda's analysis, but is not met by several examples, for instance liquid-vapor phase transitions. We examine here the stability of those interfaces that do not satisfy the uniform stability assumption, and show how Majda's results extend to such discontinuities.


We first show the linear stability of weakly stable planar shocks,
using a degenerate Kreiss' symmetrizer that takes the neutrally
unstable modes into account. This first step states precisely
the losses of derivatives in the energy estimates. Next, we show
that these estimates remain valid when dealing with the linear
stability of nonplanar interfaces that are close to a planar
shock. The use of paradifferential calculus allows us to deal
with low regularity perturbations of the reference planar shock.
Under a smallness assumption on the global behavior of the
bicharacteristic curves, we show an energy estimate that is
similar to the one derived for the constant coefficients
linearized problem. This result should enable us to prove
the nonlinear stability of weakly stable shock waves.
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https://tel.archives-ouvertes.fr/tel-00002134
Contributor : Jean-Francois Coulombel <>
Submitted on : Monday, December 16, 2002 - 4:54:09 PM
Last modification on : Wednesday, November 20, 2019 - 7:31:26 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 7:00:17 PM

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  • HAL Id : tel-00002134, version 1

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Jean-François Coulombel. Stabilite multidimensionnelle d'interfaces dynamiques. Application aux transitions de phase liquide-vapeur.. Mathématiques [math]. Ecole normale supérieure de lyon - ENS LYON, 2002. Français. ⟨tel-00002134⟩

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