The present paper concerns the study of a Riemann problem for the conservation law ut + [ϕ (u)]x = kδ (x − vt) where x, t, k, v and u = u(x,t) are real numbers. We consider ϕ an entire function taking real values on the real axis and δ stands for the Dirac measure. Within a convenient space of distributions we will explicitly see the possible emergence of waves with the shape of shock waves, delta waves and delta shock waves. For this purpose, we define a rigorous concept of a solution which extends both the classical solution concept and a weak solution concept. All this framework is developed in the setting of a distributional product that is not constructed by approximation. We include the main ideas of this product for the reader’s convenience. Recall that delta shock waves are relevant physical phenomena which may be interpreted as processes of concentration of mass or even as processes of formation of galaxies in the universe.

中文翻译：

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具有脉冲移动源的守恒律中的 Delta 激波：通过乘法分布得到的一些结果

本论文涉及对守恒定律 ut + [ϕ (u)]x = kδ (x − vt) 的黎曼问题的研究，其中 x, t, k, v 和 u = u(x,t) 是实数. 我们认为 ϕ 是一个在实轴上取实值的完整函数，δ 代表 Dirac 测度。在一个方便的分布空间内，我们将明确地看到可能出现具有冲击波、δ 波和 δ 冲击波形状的波。为此，我们定义了一个严格的解概念，它扩展了经典解概念和弱解概念。所有这些框架都是在非近似构建的分布式产品的背景下开发的。为了读者的方便，我们包含了该产品的主要思想。