论文标题
非本地保护定律对局部保护法近似的总体结果：指数核的单数极限问题
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
论文作者
论文摘要
我们处理通过非本地通量的保护法近似标量保护法的问题。作为非局部通量中的卷积内核，我们考虑了狄拉克分布的指数型近似。这使我们能够在非本地项上获得总差异。通过使用此功能，我们证明了非局部问题的（唯一）弱解决方案在$ c（l^{1} _ {\ text {loc}}}）中加剧了本地保护定律的熵解决方案。我们以几个数值插图的方式结束，这些数字插图强调了主要结果，尤其是解决方案和非局部项之间的差异。
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. This enables us to obtain a total variation bound on the nonlocal term. By using this, we prove that the (unique) weak solution of the nonlocal problem converges strongly in $C(L^{1}_{\text{loc}})$ to the entropy solution of the local conservation law. We conclude with several numerical illustrations which underline the main results and, in particular, the difference between the solution and the nonlocal term.
