Abstract This paper is concerned with the construction of global measure-valued solutions to the extended Riemann problem for a non-strictly hyperbolic system of two conservation laws with delta-type initial data. The wave interaction problems have been extensively studied for all kinds of situations by using the initial condition consisting of constant states in three pieces instead of delta-type initial data under the perturbation method. The measure-valued solutions of the extended Riemann problem are achieved constructively when the perturbed parameter tends to zero. During the process of constructing solutions, a new and interesting nonlinear phenomenon is discovered, in which the initial Dirac delta function travels along the trajectory of either delta shock wave or contact discontinuity (or delta contact discontinuity). Moreover, a delta shock wave is separated into a delta contact discontinuity and a shock wave during the process of delta shock wave penetrating a composite wave composed of a rarefaction wave and a contact discontinuity. In addition, we further consider the constructions of global measure-valued solutions when the initial condition contains Dirac delta functions at two different initial points.

中文翻译：

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具有 Delta 型黎曼初始数据的非严格双曲线系统的测值解

摘要 本文涉及为具有 delta 型初始数据的两个守恒定律的非严格双曲系统的扩展黎曼问题构建全局测度值解。在微扰方法下，利用由三部分恒定状态组成的初始条件代替δ型初始数据，对各种情况下的波浪相互作用问题进行了广泛的研究。当扰动参数趋于零时，扩展黎曼问题的测度值解是建设性地实现的。在构造解的过程中，发现了一个新的有趣的非线性现象，其中初始狄拉克 delta 函数沿着 delta 冲击波或接触不连续（或 delta 接触不连续）的轨迹传播。而且，δ激波在穿透由稀疏波和接触不连续组成的复合波的过程中被分离为δ接触不连续和激波。此外，当初始条件包含两个不同初始点的狄拉克 delta 函数时，我们进一步考虑了全局测值解的构造。