In this article, we show the global existence of solution for some semi-discrete finite difference schemes of some model system of quasilinear hyperbolic balance laws with the Cattaneo law. In [10] and [11] the first author proposed the energy method for the structure-preserving fully discrete numerical schemes for semilinear partial differential equations. The result here gives its application to quasilinear partial differential equations.

中文翻译：

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一类拟线性双曲平衡律的半离散格式的整体存在性

在本文中，我们显示了带有Cattaneo定律的拟线性双曲平衡定律模型系统的某些半离散有限差分方案的整体解。在[10]和[11]中，第一作者提出了一种能量方法，用于半线性偏微分方程的结构保全离散数值格式。此处的结果将其应用于拟线性偏微分方程。