Eulerian and Lagrangian formulations in $BV^s$ for gas-solid chromatography

Christian Bourdarias (1) , Marguerite Gisclon (1) , Stéphane Junca (2, 3) , Yue-Jun Peng (4)

1 LAMA - Laboratoire de Mathématiques
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 COFFEE - COmplex Flows For Energy and Environment
4 LMBP - Laboratoire de Mathématiques Blaise Pascal

An initial-boundary value problem for a chemical system with unknown velocity related to gas chromatography is considered. The system is hyperbolic and existence of entropy solutions is achieved in fractional BV spaces: $BV^s$, $ s ≥ 1/3$, with less regularity than usual. We prove that $BV^{1/3}$ is the critical space for this problem. A Lagrangian formulation of the system for the initial value problem provides a smoothing effect in BV and uniqueness when the first gas is more active than the second one.

Mots clés: convex flux; uniqueness; conservation laws; fractional BV spaces; entropy solution; regularity; chromatography; boundary prob-lem; Lagrangian coordinates; Cauchy problem

Domaines: Equations aux dérivées partielles [math.AP]

Christian Bourdarias, Marguerite Gisclon, Stéphane Junca, Yue-Jun Peng. Eulerian and Lagrangian formulations in $BV^s$ for gas-solid chromatography. Communications in Mathematical Sciences, 2016, 14 (6), pp.1665 - 1685. ⟨10.4310/CMS.2016.v14.n6.a10⟩. ⟨hal-01258286⟩