在這篇論文中，我們考慮單一非線性守恆律的廣義黎曼問題解， 此一守恆律的源項在分佈理論中是奇異的， 代表它是delta函數和非連續函數的乘積。在這篇論文中， 我們將展示一個例子去證明此守恆律中的非守恆乘積是不穩定的。 也就是它的正則型式的積分有不同的值。當解帶有震波時，它們的值取決於震波正則模式的選取。;In this thesis, we consider the generalized Riemann solutions of scalar nonlinear balance laws with singular source terms. The source term is singular in the sense that it is a product of delta function and a discontinuous function, which is undefined in distribution. We demonstrate an example to show that the non-conservative product $a′g(u)$ is unstable in the sense that the integral of regularization $a_{\varepsilon}′g(u_{\varepsilon})$ for $a′g(u)$ may have multiple values due to the forms $a_\varepsilon$, $u_\varepsilon$ when $u$ consists of shocks.
