Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below, we deduce the evolution in the smooth case from the jump conditions at discontinuities. Moreover, the resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, to the flow of water in a canal with varying width and depth, as well as to the inviscid Euler equations in pipes with varying geometry.

中文翻译：

---

非齐次流体动力学方程中非保守积解的适定性和表征

考虑一个平衡定律，其中通量明确取决于空间变量。在跳跃不连续处，建模考虑可能会在某些数量的守恒中施加缺陷，从而导致非保守产品。下面，我们从不连续处的跳跃条件推断出平滑情况下的演变。此外，由此产生的框架享有良好的地位，解决方案具有独特的特征。例如，这些结果适用于不同宽度和深度的运河中的水流，以及不同几何形状的管道中的非粘性欧拉方程。