This paper studies isentropic solutions of quasilinear first-order equations with two independent variables and a flux function that is only continuous. The isentropic solutions are characterized by the requirement that the S. N. Kruzhkov entropy conditions hold for these solution with the equality sign. It turns out that the existence of a nonconstant isentropic solution imposes rather strong restrictions on the nonlinearity. In particular, it is shown that on the minimal interval containing the essential image of the isentropic solution, the flux function satisfies the local Lipschitz condition, and its generalized derivative is a function of locally bounded variation. Also, it is proved that when the flux function is nonlinear, any isentropic solution is continuous on nondegenerate intervals.
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机译：本文研究具有两个独立变量和仅连续的通量函数的拟线性一阶方程的等熵解。等熵解的特征是要求S. N. Kruzhkov熵条件对于具有等号的这些解成立。事实证明，非恒定等熵解的存在对非线性施加了相当强的约束。特别地，表明在包含等熵溶液的基本图像的最小间隔上，通量函数满足局部Lipschitz条件，并且其广义导数是局部有界变化的函数。此外，证明了当通量函数为非线性时，任何等熵解都是在非退化区间上连续的。
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