非线性纤维丛上拟线性一阶方程解的熵条件，特别是二维平面射影结构方程。I
Entropy conditions for quasilinear first order equations on nonlinear fiber bundles with special emphasis on the equation of 2D flat projective structure. I
摘要：
以Arnold的"常微分方程理论中的几何方法"为精神，（Springer，1988）中，我们给出了一阶拟线性方程的广义变分熵不等式的一个独立于坐标的形式，它在局部上可读作Kruzhkov不等式，用一定的"熵密度"表示，在平面射影结构方程的情况下，利用平面的射影几何，由其抽象的激波Rankine-Hugoniot规则得到了广义熵密度的表达式。
英文摘要：
Taking only the characteristics as absolute, in the spirit of Arnold's "Geometrical Methods in the Theory of Ordinary Differential Equations" (Springer, 1988), we give an independent of coordinates formulation of general variational entropy inequalities for quasilinear equations of first order, that locally read as Kruzhkov inequalities, in terms of certain "entropy densities", and in the case of the equation of 2D flat projective structure we get the expression of the general entropy density from its abstract Rankine-Hugoniot rule for shocks using the projective geometry of the plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
