On the attainable set for a class of triangular systems of conservation laws

Abstract

We explore attainability for a special class of triangular systems of conservation laws, not necessarily strictly hyperbolic, which includes the system of multi-component chromatography. Roughly speaking, such systems consist of linear continuity equations coupled with a scalar genuinely nonlinear conservation law. The classical Keyfitz–Kranzer system is also included, with minor modifications. We prove that the backward solutions we construct are appropriate solutions of the system in view of the classical theories for general conservation laws. In particular, we get isentropic solutions whenever nontrivial entropies for the system are defined. We give numerical examples of the isentropic backward resolution of such systems for attainable target data.