The Riemann Problem For The One-dimensional Nonlinear Chromatography Equations And The Interactions Of Elementary Waves

This article mainly discussed some mathematical theory research to the one-dimen-sional nonlinear hyperbolic systems of conservation laws. In real life, owing to abundant physical significance and practical application of the chromatography, so chromatography equations has become a hot topic in recent years. This paper will focus on discussing the Riemann problem and the interactions of elementary waves of chromatography systems.In the first chapter, we mainly introduced the phenomenon of hyperbolic conservation laws that exist in cosmic space, it focused on reviewing the application and development of chromatography equations recently.In the second chapter, we are concerned with the Riemann problem of the one-dimensional nonlinear chromatography equations that widely applied to chemical and engineering fields. The most important is analyze the formation of discontinuity solution-delta shock wave solution, and obtain the delta shock wave solution constructively then prove the existence and the uniqueness of solution.In the third chapter, we study the interactions of elementary waves of another one-dimensional nonlinear chromatography equations with the method of characteristic anal-ysis and phase-plane analysis. We constructively obtain the global solutions when the initial data are three piecewise constant states. Moreover, we get the stability of the Riemann solutions by letting perturbed parameter e tend to zero.