By introducing a triple parameter flux perturbation including pressure in the modified Chaplygin gas equations, we prove that, as the triple parameter flux perturbation vanishes, any two-shock Riemann solution and any two-rarefaction-wave Riemann solution to the perturbed modified Chaplygin gas equations tend to a delta-shock and a vacuum solution to the transport equations, respectively. Then we show that, as a double parameter flux perturbation vanishes, any two-shock Riemann solution under a certain condition to the perturbed modified Chaplygin gas equations tends to a delta shock wave solution to the generalized Chaplygin gas equations. In addition, we also show that, as a single parameter flux perturbation vanishes, any two-shock solution satisfying certain initial data and any parameterized delta shock wave solution to the perturbed generalized Chaplygin gas equations tend to a delta shock wave solution to the generalized Chaplygin gas equations. Finally, we exhibit some representative numerical simulations to confirm the theoretical analysis.

中文翻译：

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三角波作为修正的Chaplygin气体方程解的通量近似极限

通过在修改后的Chaplygin气体方程中引入包含压力的三参数通量扰动，我们证明，随着三参数通量扰动的消失，被扰动的修改后Chaplygin气体方程式中将出现任何两波Riemann解和任何两次反射波Riemann解。趋向于分别对输运方程产生delta-shock和真空解。然后我们表明，随着双参数通量扰动的消失，在一定条件下对经修正的Chaplygin气体方程组的任何两冲击Riemann解都趋向于对广义Chaplygin气体方程组的三角波冲击解。此外，我们还表明，随着单参数通量扰动的消失，满足某些初始数据的任何两冲击解以及对扰动的广义Chaplygin气体方程的任何参数化的delta冲击波解都趋向于对广义Chaplygin气体方程的delta冲击波解。最后，我们展示一些有代表性的数值模拟以证实理论分析。