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# Communications in Mathematical Sciences

## Volume 14 (2016)

### Number 6

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

Pages: 1665 – 1685

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n6.a10

#### Authors

#### Abstract

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: $BV^s , s \geq 1/3$, 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.

#### Keywords

chromatography, conservation laws, fractional $BV$ spaces, boundary problem, convex flux, entropy solution, Lagrangian coordinates, Cauchy problem, uniqueness, regularity

#### 2010 Mathematics Subject Classification

35B44, 35B65, 35L65, 35L67