Existence Of Global Smooth Solution To System Of Hyperbolic Conservation Laws In Two Component Chromatography

In this paper, we consider the existence of global smooth solutions to the Cauchy problem for the following nonlinear hyperbolic conservation laws arising in two component chromatographywith initial datau(x, 0)=u₀(x), v(x, 0)=v₀(x). (0.2)In system (0.1), x and t respectively denote transformations of the actual space and time variables.The analysis is based on the diagonalization method and the characteristic method.This paper is made up of three chapters.In chapter one, we introduce the background of nonlinear hyperbolic conservation laws arising in two component chromatography and the relevant research progress, furthermore, we state our main results. In chapter two, we prove the existence and uniqueness of the global smooth solutions to the diagonalization equations correspond to system(0.1) by employing the characteristic method. In chapter three, under the assmption of the initial data u₀(x),v₀(x), based on the characteristic method, we prove that the Cauchy problem (0.1), (0.2) admits a unique global smooth solution by introducing Riemann invariants.