In this work, we study Riemann problems and delta-shock solutions for a nonsymmetric Keyfitz-Kranzer system with a Coulomb-like friction term or linear damping. We show the existence of an intricate delta-shock wave solution and its generalized Rankine-Hugoniot condition resulting from the analysis. In particular, we also show the existence of a shock wave solution satisfying the classical Rankine-Hugoniot condition and the Lax shock condition, which is supported by the corresponding homogeneous Keyfitz-Kranzer system under investigation. Some numerical results exhibiting the formation process of delta-shocks are also presented, verifying the theory being presented. In particular, the robustness of the numerics is illustrated with a very interesting linear damping example, where we show a simulation of the cutoff time in which a delta-shock singular solution ceases to exist, and in fully agreement with the theoretical results.

在这项工作中，我们研究具有库仑式摩擦项或线性阻尼的非对称Keyfitz-Kranzer系统的Riemann问题和delta-shock解。我们显示了一个复杂的三角波冲击波解的存在及其从分析中得出的广义兰金-休格尼奥特条件。尤其是，我们还显示了满足经典兰金-休格尼奥特条件和Lax冲击条件的冲击波解的存在，并得到了相应的均质Keyfitz-Kranzer系统的支持。还给出了一些反映三角波冲击形成过程的数值结果，验证了所提出的理论。特别是，通过一个非常有趣的线性阻尼示例说明了数字的鲁棒性，