色谱方程的广义黎曼问题:含有Delta激波

The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave

论文研究了非线性色谱方程的广义黎曼问题,并在x-t平面内,构造性地获得了上述广义黎曼问题的局部解.由于非线性色谱方程的黎曼解含有Delta激波,这与以往其它模型的广义黎曼问题(对应的黎曼解只有古典基本波)有很大区别.论文结果表明:在大多情况,广义黎曼解和对应的黎曼解结构相同;但当相关的黎曼解含有Delta激波时,Delta激波可能会转变成激波和接触间断的组合.论文结果有助于详细分析Delta激波的内部机理.

This paper is concerned with the generalized Riemann problem for the nonlinear chromatography equations,where the delta shock wave occurs in the corresponding Riemann solution.It is quite different from the previous generalized Riemann problems which focus on classical elementary waves.We constructively solve the generalized Riemann problem in a neighborhood of the origin on the x−t plane.In solutions,we find that the generalized Riemann solutions have a structure similar to the solution of the corresponding Riemann problem for most of cases.However,a delta shock wave in the corresponding Riemann solution may turn into a shock wave followed by a contact discontinuity,which provides us with a detailed method for analyzing the internal mechanism of a delta shock wave.