Existence and Stability of travelling
Waves Solutions in a Kinetic Model
of Two-phase Flows

   K.Demelevo
   J.M.Roquejoffre

This work is aimed at proving the nonlinear stability of a kinetic model
for a two-phase fluid flow describing the motion of a spray in a gas.
The gas motion is described by the viscous Burgers' equation, and the spray
by a linear transport equation. Finally, the two phases exchange momentum.
In this paper we first prove the global existence and uniqueness of regular
solutions of the system. Then, we prove the existence of travelling waves
and their stability. The travelling waves appear to be singular
solutions of the system and the component of the wave for the spray is a bounded
measure. Then, we prove the linear stability of the wave, where the
scaling used for the spray corresponds to a dilation.
Then, adapting the ideas of Sattinger, we prove the nonlinear stability
under small perturbations.The whole paper is available as a compressed Postscript file by internet
procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100)
in the directory pub/RI/1996 under the name

        
            domelevo_roquejoffre_353.july.ps.gz

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