In this paper, we explore the Riemann problem for the equations of constant pressure fluid dynamics with nonlinear damping. By introducing a variable substitution of exponential type, the Riemann problem is solved and the solutions involving delta shock wave and vacuum state are obtained. Then, we solve the generalized Riemann problem for such equations with nonlinear damping when the initial data contain a Dirac delta function, and obtain four kinds of different structures for solutions. Particularly, the influence of the nonlinear external source terms on Riemann solutions are analyzed.

中文翻译：

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具有非线性阻尼的恒压流体动力学方程的Riemann问题。

在本文中，我们探讨了带有非线性阻尼的恒压流体动力学方程的黎曼问题。通过引入指数类型的变量替换，解决了黎曼问题，并获得了涉及三角波和真空状态的解。然后，当初始数据包含狄拉克三角函数时，我们用非线性阻尼求解了这类方程的广义Riemann问题，并获得了四种不同的结构进行求解。特别是，分析了非线性外部源项对黎曼解的影响。