标题： 对使用影子波和Dafermos正则化求解Keyfitz-Kranzer型守恒律$2 \times 2$系统的Riemann问题的分析 显示英文标题

标题： An Analysis of the Riemann Problem for a $2 \times 2$ System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization

摘要： 我们考虑一个由两个守恒定律组成的系统，并提供了对经典和非经典自相似黎曼解的详细描述。 特别是，我们展示了超压缩δ冲击波作为该系统达弗莫斯正则化的奇异极限的存在性。 该系统被选择是因为其最小但具有代表性的结构，能够捕捉密度约束下传输动力学的基本特征。 我们的分析是在几何奇异性摄动理论（GSPT）框架内使用爆破技术进行的，使我们能够解析这些奇异解的内部结构。 尽管其结构简单，该系统却作为一个通用的原型，在多种应用中用于拥挤限制下的传输，包括生物聚集、生态扩散、颗粒压实和交通拥堵。 我们的研究结果得到了使用局部拉克斯-弗里德里希斯格式进行数值模拟的支持。 显示英文摘要

摘要： We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular limits of the Dafermos regularization of the system. The system is chosen for its minimal yet representative structure, which captures the essential features of transport dynamics under density constraints. Our analysis is carried out using blow-up techniques within the framework of Geometric Singular Perturbation Theory (GSPT), allowing us to resolve the internal structure of these singular solutions. Despite its simplicity, the system serves as a versatile prototype for crowding-limited transport across a range of applications, including biological aggregation, ecological dispersal, granular compaction, and traffic congestion. Our findings are supported by numerical simulations using the Local Lax-Friedrichs scheme.