The Global Solution Of The Initial-Boundary Value Problem For Nonlinear Chromatography Systems Of Two Components

Chromatographer is a new analytical technique which has developed recently, it has extensive application in the science experiment and public economy fields. The key technique of chromatography model is the initial-boundary value problem of nonlinear hyperbolic conservation laws systems. because of the high nonlinear of the problem and the complexity of the described physics phenomenon, it is very significative to study. In this paper, according to the actual problem of the chromatography, we establish the mathematics models of nonlinear chromatography of two components, and study the initial-boundary value problem of the hyperbolic conservation laws systems to which nonlinear chromatography of two components correspond. Firstly, by appropriate transform, nonlinear chromatography equations of two components are changed to normal hyperbolic conservation laws systems, and by getting eigenvalues and eigenvectors of the equations, we deduce the equations are genuinely nonlinear. Secondly, according to the frame of the nonlinear hyperbolic conservation laws systems' weak solution, we get the solutions' expressions of general Riemann initial-boundary value problems. By analyzing interactions of elementary waves, we deduce in detail the global solutions' expressions of special initial-boundary value problems corresponding to the two types important actual problem of frontal method and wide pulse including the characteristic velocity of concentration wave, and the velocity of the shock wave, and the retention time, and the elution curve so on. Because of complexity of the solutions' expressions—implicit function equations, parameter equations and dynamic subsection function etc, aiming at these problems, we give relevant arithmetic, and using Microsoft Office Excel 2003 and Origin 6.0 etc, we get numerical simulation of the wave shapes of elution curves.