论文标题
非本地标量保护定律准室内溶液的稳定性
Stability of quasi-entropy solutions of non-local scalar conservation laws
论文作者
论文摘要
我们证明了非线性保护定律的熵解决方案在初始基准，时空依赖性通量和熵不平等方面的扰动。 这样的一般稳定性定理是由研究磁通量$ p [u]（t，x，u）$的问题的动机，这可能非局部取决于解决方案本身。对于这些问题，我们显示了熵解决方案的条件存在和独特性。 此外，熵不平等的松弛允许处理由各种数值方案引起的近似解。这可以用于得出[Radici-Stra 2021]中介绍的最近粒子方法的收敛速率，以解决一种交通拥堵的一维流量模型，并为其他一些近似方法恢复了已知的速率。
We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux $P[u](t,x,u)$ depends possibly non-locally on the solution itself. For these problems we show the conditional existence and uniqueness of entropy solutions. Moreover, the relaxation of the entropy inequality allows to treat approximate solutions arising from various numerical schemes. This can be used to derive the rate of convergence of the recent particle method introduced in [Radici-Stra 2021] to solve a one-dimensional model of traffic with congestion, as well as recover already known rates for some other approximation methods.
