Regularity estimates for scalar conservation laws in one space dimension
Regularity estimates for scalar conservation laws in one space dimension
复制标题
一维标量守恒定律的正则估计
DOI：
--
复制
发表时间：
2017
影响因子：
0.7
通讯作者：
Elio Marconi
中科院分区：
文献类型：
--
作者：
Elio Marconi
我们处理的正则化效果，在标量守恒律在一个空间维度，非线性的通量函数[公式：见正文]上的熵的解决方案。更准确地说，如果集合[Formula：see text]是稠密的，解的正则性可以用[Formula：see text]空间来表示，其中[Formula：see text]依赖于[Formula：see text]的非线性。此外，如果集合[公式：见正文]是有限的，在拐点处的附加多项式退化条件下，我们证明了[公式：见正文]对每个[公式：见正文]，这可以改进为[公式：见正文]正则性，除了至多可数的奇异时间集。最后，我们提出了一些例子，这些结果和反例的清晰度相关的问题，即规律性的动力学制定和性质的分数BV空间。
We deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function [Formula: see text] has on the entropy solution. More precisely, if the set [Formula: see text] is dense, the regularity of the solution can be expressed in terms of [Formula: see text] spaces, where [Formula: see text] depends on the nonlinearity of [Formula: see text]. If moreover the set [Formula: see text] is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that [Formula: see text] for every [Formula: see text] and that this can be improved to [Formula: see text] regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.