Shock Wave for the Simplified Chromatography Equations
In this paper,we investigate the formation and the well-posedness of the shock solution for the simplified chromatography equations.Firstly,under certain conditions,we prove that the derivatives of the solution for the Cauchy problem will blow up in finite time by using the method of characteristic decomposition,i.e.,the shock wave occurs.Secondly,we demonstrate the shock wave solution's existence,uniqueness,and stability using the self-similar viscosity vanishing approach.Moreover,some representative numerical simulations are given.
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