论文标题
保护法律系统的能源耗散可接纳性条件承认单数解决方案
Energy dissipation admissibility condition for conservation law systems admitting singular solutions
论文作者
论文摘要
本文的主要目的是定义和使用足以在初始数据中具有单一度量的保护法律系统的独特解决方案。不同的近似可能会导致具有不同分布限制的解决方案。然后，称为向后能量条件的新概念是要挑选出分布初始数据的适当近似值。该定义基于\ cite {cd_1973}中定义的最大能量耗散。假设保护法系统以空间分歧形式接受补充法律，其中时间成分是（是否严格）凸功能。例如，它可能是气体动态模型中的能量密度或数学熵。可接受性的条件之一是，适当的弱解决方案应最大程度地消散能量或数学熵。我们表明，在本文第一部分中，具有非阳性压力的等性气体动力学系统的Riemann问题，这与其他可接受性条件是一致的。这些系统的单数解用阴影波描述，相对于时间变量，分段恒定近似值的网。在第二部分中，当初始数据包含通过分段常数函数近似的DELTA度量时，我们为这些系统定义并应用了向后的能量条件。
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different distributional limits. The new notion called backward energy condition is then to single out a proper approximation of the distributional initial data. The definition is based on the maximal energy dissipation defined in \cite{CD_1973}. Suppose that a conservation law system admits a supplementary law in space--time divergent form where the time component is a (strictly or not) convex function. It could be an energy density or a mathematical entropy in gas dynamic models, for example. One of the admissibility conditions is that a proper weak solution should maximally dissipate the energy or the mathematical entropy. We show that it is consistent with other admissibility conditions in the case of Riemann problems for systems of isentropic gas dynamics with non-positive pressure in the first part of the paper. Singular solutions to these systems are described by shadow waves, nets of piecewise constant approximations with respect to the time variable. In the second part, we define and apply the backward energy condition for those systems when the initial data contains a delta measure approximated by piecewise constant functions.
