Nonlocal Traffic Models with General Kernels: Singular Limit, Entropy Admissibility, and Convergence Rate
Nonlocal Traffic Models with General Kernels: Singular Limit, Entropy Admissibility, and Convergence Rate
复制标题
具有通用内核的非局部流量模型：奇异极限、熵容许性和收敛率
DOI：
10.1007/s00205-023-01845-0
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发表时间：
2022
影响因子：
2.5
通讯作者：
L. Spinolo
中科院分区：
文献类型：
--
作者：
Maria Colombo;Gianluca Crippa;Elio Marconi;L. Spinolo
非局部守恒律（其特征是通量函数依赖于与给定核卷积的解）广泛用于车辆交通建模。在这项工作中，我们讨论了奇异的局部极限，即收敛的非局部解决方案的熵容许的解决方案的守恒律取代卷积核与狄拉克δ。虽然最近的反例排除了一般情况下的收敛性，但在流量模型（具有各向异性卷积核）的特定框架中，奇异极限已在严格假设下建立，即在指数核（需要核及其导数之间的代数恒等式）的情况下或在对初始数据的相当严格的要求下。在这项工作中，我们得到了一般的收敛结果的假设下，是完全自然的交通模型的应用程序，加上凸性要求的卷积核。然后，我们提供了一个熵容许的极限和收敛速度的一般标准。我们还展示了一个反例表明，凸性假设是必要的，我们的主要紧性估计。
Nonlocal conservation laws (the signature feature being that the flux function depends on the solution through the convolution with a given kernel) are extensively used in the modeling of vehicular traffic. In this work we discuss the singular local limit, namely the convergence of the nonlocal solutions to the entropy admissible solution of the conservation law obtained by replacing the convolution kernel with a Dirac delta. While recent counter-examples rule out convergence in the general case, in the specific framework of traffic models (with anisotropic convolution kernels) the singular limit has been established under rigid assumptions, i.e. in the case of the exponential kernel (which entails algebraic identities between the kernel and its derivatives) or under fairly restrictive requirements on the initial datum. In this work we obtain general convergence results under assumptions that are entirely natural in view of applications to traffic models, plus a convexity requirement on the convolution kernels. We then provide a general criterion for entropy admissibility of the limit and a convergence rate. We also exhibit a counter-example showing that the convexity assumption is necessary for our main compactness estimate.
影响因子：
1
作者：
Bressan, Alberto;Shen, Wen
通讯作者：
Shen, Wen
影响因子：
2.4
作者：
Alexander Keimer;L. Pflug
通讯作者：
Alexander Keimer;L. Pflug