论文标题
与BV空间通量和潘诺夫类型通量的研究，戈努维的戈努维方案的融合
Convergence of a Godunov scheme for degenerate conservation laws with BV spatial flux and a study of Panov type fluxes
论文作者
论文摘要
在本文中，我们证明了[16]的Godunov方案在一个空间维度中具有标量保护定律，并具有空间不连续的通量。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。与[16]中出现的研究相反，我们不限制通量是单峰的。我们允许通量具有变性的情况，即通量可能会在某个状态空间间隔消失。由于允许通量退化，因此相应的奇异图可能不可逆转，因此[16]中出现的收敛性证明无关。我们证明，戈杜诺夫近似仍然使用替代的证明方法在磁衰变的情况下会融合。我们还考虑了通量具有[21]中描述的形式的情况。对于这种情况，我们通过另一种方法证明了收敛。这种证明方法提供了在解决方案上绑定的空间变化，这具有独立的兴趣。我们提出了说明理论的数值示例。
In this article we prove convergence of the Godunov scheme of [16] 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 contrast to the study appearing in [16], we do not restrict the flux to be unimodal. We allow for the case where the flux has degeneracies, i.e., the flux may vanish on some interval of state space. Since the flux is allowed to be degenerate, the corresponding singular map may not be invertible, and thus the convergence proof appearing in [16] does not pertain. We prove that the Godunov approximations nevertheless do converge in the presence of flux degeneracy, using an alternative method of proof. We additionally consider the case where the flux has the form described in [21]. For this case we prove convergence via yet another method. This method of proof provides a spatial variation bound on the solutions, which is of independent interest. We present numerical examples that illustrate the theory.
