### HYPERBOLIC MODELS IN GAS-SOLID CHROMATOGRAPHY

*C. Bourdarias, M. Gisclon, S. Junca*

#### Resumen

*CHRISTIAN BOURDARIAS, MARGUERITE GISCLON AND STÉPHANE JUNCA†*

Laboratoire de Mathématiques, UMR CNRS 5127 Université de Savoie. 73376 Le Bourget-du-Lac Cedex, France, †Laboratoire JAD, UMR CNRS 6621, IUFM et Universit´e de Nice. Parc Valrose, 06108 Nice

We present different models arising in chemical engineering and essentially related to isothermal gas chromatography. These models describe a fixed bed adsorption process of separation of a gaseous mixture: each compound can exist either in a mobile phase or a solid and static one, with a finite or infinite mass-exchange kinetics. Many authors, in the fields of chemical engineering and mathematics, have investigated these models under various assumptions, from a theoretical or numerical point of view. We explain first the relations between some of these approaches. Next, we present some results related to these models, some of them being new, particularly in the case of a monovariant system with one or two active compounds for the Cauchy problem. Lastly, we mention some open problems.

**Key words:** gas chromatography, nonlinear chromatography, mass transfer kinetics, adsorption, systems of conservation laws.

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