论文标题
具有空间异质性和BV规律性的保护法的适应性良好
Well-posedness for conservation laws with spatial heterogeneities and a study of BV regularity
论文作者
论文摘要
在本文中，我们考虑了具有空间不连续性和可能的扁平区域的通量的标量保护定律，并研究了以下三个方面：（i）存在，（ii）唯一性和（iii）解决方案的唯一性和（iii）。我们提出了独特的条件，并通过波前跟踪方法证明了弱解的存在。在本文的后面部分，在初始数据和通量的适当条件下实现了解决方案的BV界限。我们构建了两个反示例，显示了解决方案的BV爆炸，这证明了假设的最佳性
In this article, we consider scalar conservation laws with fluxes having spatial discontinuities and possible flat regions and study the following three aspects: (i) existence, (ii) uniqueness and (iii) BV regularity of solutions. We propose a uniqueness condition and prove existence of a weak solution via the method of wave front tracking. In the later part of the article, a BV bound of the solution is achieved under a suitable condition on the initial data and flux. We construct two counterexamples showing BV blow-up of the solution which proves the optimality on the assumptions
