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Wave interactions and stability of the Riemann solutions for the chromatography equations. (English) Zbl 1184.35207
Summary: We prove that the Riemann solutions are stable for the chromatography system under the local small perturbations of the Riemann initial data. The proof is based on the detailed analysis of the wave interactions by applying the method of characteristic analysis. It is noteworthy that both the propagation directions of the shock wave $S$ and rarefaction wave $R$ are unchanged when they interact with the contact discontinuity $J$. Moreover, the global structures and large time asymptotic behaviors of the perturbed Riemann solutions are constructed and analyzed case by case.

35L67Shocks and singularities
35L65Conservation laws
35B35Stability of solutions of PDE
Full Text: DOI
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