In this work, we are dealing with a non-linear eikonal system in one dimensional space that describes the evolution of interfaces moving with non-signed strongly coupled velocities. For such kind of systems, previous results on the existence and uniqueness are available for quasi-monotone systems and other special systems in Lipschitz continuous space. It is worth mentioning that our system includes, in particular, the case of non-decreasing solution where some existence and uniqueness results arose for strictly hyperbolic systems with a small total variation. In the present paper, we consider initial data with unnecessarily small $ BV $ seminorm, and we use some $ BV $ bounds to prove a global-in-time existence result of this system in the framework of discontinuous viscosity solution.

中文翻译：

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\ begin {document} $ BV $ \ end {document} 非线性Hamilton-Jacobi系统的解

在这项工作中，我们正在处理一维空间中的非线性本征系统，该系统描述了以无符号强耦合速度运动的界面的演化。对于这样的系统，关于存在性和唯一性的先前结果可用于拟单调系统和Lipschitz连续空间中的其他特殊系统。值得一提的是，我们的系统尤其包括非递减解的情况，其中严格的双曲型系统的总变化量很小，因此存在一些存在性和唯一性。在本文中，我们考虑具有$ BV $半范数不必要小的初始数据，并使用一些$ BV $边界来证明该系统在不连续粘度解的框架中的全局时间存在结果。