The Global Solution Of The Initial-Boundary Value Problem For A Class Of Reaction Chromatography Systems

The key technique of reaction chromatography is the initial boundary value problem for 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 them. In this paper, according to the actual problem of the reaction chromatography, we establish the mathematics models of several types reaction chromatography. Take A →B type reaction chromatography as an example, we research the initial-boundary value problem of the non-homogeneous hyperbolic conservation laws systems that linear and nonlinear ideal reaction chromatography equations respectively. Firstly, making use of the method of characteristics, we give the solution of generally initial-boundary value problem for linear ideal reaction chromatography equations, and deduce the expression of the solutions of several types actual problem detailed. Secondly, by handling appropriately, the nonlinear ideal reaction chromatography equations are changed to two independence nonlinear hyperbolic conservation laws. Take the nonlinear systems of reaction density c₁ as an example, we detailed study the characteristic line's establishment method, and the property of the characteristic line, proof the necessary and sufficiency condition of the characteristics intersection. According to the frame of the nonlinear hyperbolic conservation laws initial value problem's weak solution, we give the definition for responding...