论文标题
与不连续的保存法律的分数规律性
Fractional regularity for conservation laws with discontinuous flux
论文作者
论文摘要
本文介绍了不连续的标量保护法的熵解决方案的规律性。它是众所周知的[Adimurthi等，Comm。纯应用。数学。 [2011年]，即使初始数据属于BV，这种方程式的熵解决方案也不会接受BV规律性。由于这种现象，需要比BV宽，其中指数为0 <s \ leq 1和bv = bv1。这是一个长期的开放问题，可以找到具有L^\ Infty初始数据的不连续通量的最佳正规化效果。在使用控制理论的重要情况下证明了BVS中最佳的正规化效果。即使通量均匀凸出，分数指数s最多也是1/2。
This article deals with the regularity of the entropy solutions of scalar conservation laws with discontinuous flux. It is well-known [Adimurthi et al., Comm. Pure Appl. Math. 2011] that the entropy solution for such equation does not admit BV regularity in general, even when the initial data belongs to BV. Due to this phenomenon fractional BVs spaces wider than BV are required, where the exponent 0<s\leq 1 and BV = BV1. It is a long standing open question to find the optimal regularizing effect for the discontinuous flux with L^\infty initial data. The optimal regularizing effect in BVs is proven on an important case using control theory. The fractional exponent s is at most 1/2 even when the fluxes are uniformly convex.
