论文标题
关于不连续的非本地保护法的单数极限问题
On the singular limit problem for a discontinuous nonlocal conservation law
论文作者
论文摘要
在这项贡献中，我们研究了非本地保护定律的单一极限问题，其空间不连续。涉及空间不连续性的非局部内核的具体选择也使其能够获得非局部方程的最大原理。相应的局部方程可以分散地转换为经典的标量保护定律，在该定律中可以应用众所周知的Kružkov理论。但是，非局部方程并不是这样扩展的，这就是为什么融合研究有趣的原因。对于非局部运算符中的指数核，我们在涉及的不连续速度下在轻度条件下建立了融合到相应的局部方程。我们用一些数值示例来说明结果。
In this contribution we study the singular limit problem of a nonlocal conservation law with a discontinuity in space. The specific choice of the nonlocal kernel involving the spatial discontinuity as well enables it to obtain a maximum principle for the nonlocal equation. The corresponding local equation can be transformed diffeomorphically to a classical scalar conservation law where the well-know Kružkov theory can be applied. However, the nonlocal equation does not scale that way which is why the study of convergence is interesting to pursue. For exponential kernels in the nonlocal operator, we establish the converge to the corresponding local equation under mild conditions on the involved discontinuous velocity. We illustrate our results with some numerical examples.
