论文标题
Godunov计划与Audusse-Perthame的适应性熵解决方案的融合，用于保存法律，用于BV空间磁通
Convergence of a Godunov scheme to an Audusse-Perthame adapted entropy solution for conservation laws with BV spatial flux
论文作者
论文摘要
在本文中，我们考虑了一个空间不连续的一个空间维度中标量保护定律的初始价值问题。可能存在无限的通量不连续性，并且不连续性可能具有积累点。因此，无法假设痕迹的存在。在[6]中，Audusse和Perthame证明了使用改编的熵不需要痕迹的独特结果。我们将Adimurthi，Jaffre和Gowda [2]的Godunov型方案概括为此问题，以下对通量功能的假设，（i）（i）空间变量中的通量为BV，并且（ii）磁通量的临界点是bv作为空间变量的函数。我们证明，戈多诺夫近似融合到适应的熵解决方案，从而提供了存在结果，并扩展了Adimurthi，Jaffre和Gowda的收敛结果。
In this article we consider the initial value problem for a scalar conservation law in one space dimension with a spatially discontinuous flux. There may be infinitely many flux discontinuities, and the set of discontinuities may have accumulation points. Thus the existence of traces cannot be assumed. In [6] Audusse and Perthame proved a uniqueness result that does not require the existence of traces, using adapted entropies. We generalize the Godunov-type scheme of Adimurthi, Jaffre and Gowda [2] for this problem with the following assumptions on the flux function, (i) the flux is BV in the spatial variable and (ii) the critical point of the flux is BV as a function of the space variable. We prove that the Godunov approximations converge to an adapted entropy solution, thus providing an existence result, and extending the convergence result of Adimurthi, Jaffre and Gowda.
