Abstract
We consider a 2n × 2n system of conservation laws with stiff relaxation terms. The system arises from the modelling of multicomponent chromatography, and the zero relaxation limit is a n × n system of conservation laws of Temple class. For initial data which are small in BV, we establish an a priori bound on the total variation of the solution, relying on a probabilistic technique. Moreover, we show that this solution depends Lipschitz continuously on the initial data in L1. These estimates are uniform w.r.t. the relaxation parameter. Finally, we prove the convergence towards equilibrium as the relaxation time tends to zero. This provides a first example where BV estimates and convergence are proved for general solutions to a class of 2n × 2n systems with relaxation.
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Bressan, A., Shen, W. (2001). The Convergence of Multicomponent Chromatography with Relaxation. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_21
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DOI: https://doi.org/10.1007/978-3-0348-8370-2_21
Publisher Name: Birkhäuser, Basel
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