Global existence of weak solutions for [formula omitted] system of chromatography.

In the paper James et al. (1995), the authors established a compact framework for general n × n system of chromatography (1.1) by using the kinetic formulation coupled with the compensated compactness method. However, how to construct suitable approximated solutions { u i l } of system (1.1) and then to prove the compactness of η ( u i l ) t + q ( u i l ) x in H l o c − 1 , for the entropy–entropy flux pairs ( η , q ) constructed by the kinetic formulation, with respect to the sequence { u i l } , is an open problem. In this paper, we construct the approximated solutions { u i ε } by using the parabolic viscosity method. By carefully calculating the Riemann invariants of system (1.1) , we obtained all necessary estimates in the compact framework of James et al. (1995), and gave a complete proof of the global existence of weak solutions for the Cauchy problem (1.1) with the bounded, nonnegative initial data (1.2) . As a direct by-product, when the total variation of the initial data is bounded, we obtained a simple proof of the existence of global weak solutions by applying the Div-Curl lemma in the compensated compactness theorem to some pairs of functions ( c , f ( u i ) ) , where c is a constant. [ABSTRACT FROM AUTHOR]