具有不连续通量的粘性守恒律的存在性、唯一性和大时间行为
Existence, uniqueness and Large time behavior of a viscous conservation law with discontinuous flux
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中文总结 AI 辅助
研究具有不连续通量的粘性守恒律，通过定义弱解概念，利用显式公式证明其存在唯一性，还得到解的大时间行为，其渐近极限是稳态解，大时间渐近依通量函数在阈值处行为收敛到常数或非常数稳态，单通量情况无此现象。
中文摘要 AI 辅助
在本文中，我们研究了具有不连续通量的粘性守恒律。我们定义了一个弱解概念，通过显式公式证明其存在性，并证明弱解是唯一的。此外，我们还得到了解的大时间行为。解的渐近极限是一个稳态解。这里，由对流项控制的大时间渐近根据通量函数在阈值（两个通量的交汇点）处的行为，要么收敛到一个常数稳态，要么收敛到一个非常数稳态。这种现象在单通量情况下不会出现。
英文摘要
In this paper, we study a viscous conservation law with discontinuous flux. We define a weak solution concept, show its existence via an explicit formula, and prove that the weak solution is unique. In addition, we obtain the large-time behavior of the solution. The asymptotic limit of the solution is a steady-state solution. Here, the large-time asymptotic governed by the convection terms either converges to a constant steady state or to a non-constant steady state, depending on the behavior of the flux functions at a threshold value, which is the meeting point of two fluxes. This phenomenon does not occur in the single-flux case.
