论文标题
非线性双曲方程的耦合技术。 ii。具有内部结构的谐振接口
Coupling techniques for nonlinear hyperbolic equations. II. Resonant interfaces with internal structure
论文作者
论文摘要
在本系列的第一部分中，引入了一个增强的PDE系统，以将两个非线性双曲线方程式融合在一起。这种表述使作者基于Dafermos的自相似粘度方法，可以确定对耦合的Riemann问题的自相似解决方案的存在。我们在此继续在一维标量方程的{限制}情况下继续进行此分析，并研究界面的内部结构，以得出与基础正则化机制相关的选择标准，并反过来表征非保守界面层。此外，我们确定了一个新标准，该标准选择了在接口处连续连续的双波解决方案。我们通过提供一些证据表明，在处理非凸通量功能时，这种解决方案可能不是唯一的。
In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish the existence of self-similar solutions to the coupled Riemann problem. We continue here this analysis in the {restricted} case of one-dimensional scalar equations and investigate the internal structure of the interface in order to derive a selection criterion associated with the underlying regularization mechanism and, in turn, to characterize the nonconservative interface layer. In addition, we identify a new criterion that selects double-waved solutions that are also continuous at the interface. We conclude by providing some evidence that such solutions can be non-unique when dealing with non-convex flux-functions.
