BLOW UP AT THE HYPERBOLIC BOUNDARY FOR A $ 2 × 2$ SYSTEM ARISING FROM CHEMICAL ENGINEERING

Christian Bourdarias (1) , Marguerite Gisclon (1) , Stéphane Junca (2)

1 LAMA - Laboratoire de Mathématiques
2 JAD - Laboratoire Jean Alexandre Dieudonné

We consider an initial boundary value problem for a $2 \times 2$ system of conservation laws modeling heatless adsorption of a gaseous mixture with two species and instantaneous exchange kinetics, close to the system of Chromatography. In this model the velocity is not constant because the sorption effect is taken into account. Exchanging the roles of the $x, t$ variables we obtain a strictly hyperbolic system with a zero eigenvalue. Our aim is to construct a solution with a velocity which blows up at the corresponding characteristic "hyperbolic boundary" $\{t = 0\}$.

Mots clés: Temple systems; weak solutions; conservation laws; hyperbolic systems; Riemann problem; gas chromatography; blow up; boundary conditions; Front Tracking Algorithm

Domaines: Equations aux dérivées partielles [math.AP]; Génie chimique

Christian Bourdarias, Marguerite Gisclon, Stéphane Junca. BLOW UP AT THE HYPERBOLIC BOUNDARY FOR A $ 2 × 2$ SYSTEM ARISING FROM CHEMICAL ENGINEERING. Journal of Hyperbolic Differential Equations, 2010, 7 (2), pp.297-316. ⟨10.1142/S0219891610002116⟩. ⟨hal-00403226v2⟩