论文标题
在带有空间依赖系数的波方程上：奇异性和较低顺序项
On the wave equation with space dependent coefficients: singularities and lower order terms
论文作者
论文摘要
本文在\ cite {dgl：22}的情况下，在时间依赖的系数的情况下，对波方程的研究进行了补充。在这里，我们假设方程系数仅取决于空间，并且我们在较低的术语上制定了Levi条件，以确保存在\ cite {gr：14}中定义的非常弱的解决方案。作为玩具模型，我们以不连续的速度以保守形式研究波动方程，并通过数值方法对相应的非常弱的解决方案进行定性分析。
This paper complements the study of the wave equation with discontinuous coefficients initiated in \cite{DGL:22} in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Levi conditions on the lower order terms to guarantee the existence of a very weak solution as defined in \cite{GR:14}. As a toy model we study the wave equation in conservative form with discontinuous velocity and we provide a qualitative analysis of the corresponding very weak solution via numerical methods.
