不稳定shock waves的极小双曲组
A minimal hyperbolic system for unstable shock waves
摘要：
我们提出了一个计算分析的2 $\times$ 2双曲系统的平衡律，其解决方案表现出复杂的非线性行为。行波解的系统进行了一系列的分叉作为模型中的参数是变化的。线性和非线性稳定性的行波的数值计算使用精确的冲击拟合方法。该模型可以被认为是一个具有混沌解的极小双曲系统，也可以作为双曲平衡律系统的严格数值检验问题。
英文摘要：
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using accurate shock-fitting methods. The model may be considered as a minimal hyperbolic system with chaotic solutions and can also serve as a stringent numerical test problem for systems of hyperbolic balance laws.
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