Kinetic formulation for chromatography 
            and some other hyperbolic systems
 

          F. James   Y.-J. Peng   B. Perthame
Departement de Mathematiques, Faculte des Sciences,
Universite d'Orleans, BP 6759,
45067 Orleans Cedex 2, FRANCE


 
          Abstract
We present several new examples of kinetic formulations for some hyperbolic
systems, which is to write an equation for a whole family of entropies. It
appears that, in fact, several families of entropies can be represented in such
a way. For instance, in the NxN chromatography case, we obtain N+1
kinetic representations from which we recover the invariant regions and the
stability for weakly convergent initial data by a compensated compactness
argument, including the non-strictly hyperbolic case.

          Resume 
Nous presentons quelques nouveaux exemples de formulations cinetiques de
systemes hyperboliques, ce qui consiste a ecrire une equation pour
toute une famille d'entropies. Il apparait qu'en fait plusieurs familles
differentes peuvent se representer ainsi. Par exemple, dans le cas du
systeme NxN de la chromatographie, nous obtenons N+1
representations cinetiques. Nous retrouverons ainsi les zones invariantes
et la stabilite, pour des donnees initiales convergeant faiblement, grace
a un argument de compacite par compensation, incluant le
cas non-strictement hyperbolique.


Key-words : hyperbolic systems - kinetic equations -
entropy - compensated compactness - chromatography.

Mots cles : systemes hyperboliques - equations cinetiques - entropies -
 compacite par compensation - chromatographie.

AMS Class numbers : 35L65, 35L67, 35Q20

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