论文标题
汉密尔顿 - 雅各比方程在连接处的随机均质化
Stochastic homogenization of Hamilton-Jacobi equations on a junction
论文作者
论文摘要
我们考虑了非常简单的交界处的一阶进化汉密尔顿 - 雅各布方程的特定随机均质化，即具有原点连接的真实线。我们假设所考虑的汉密尔顿人对给定的固定的ergodic hamiltonians（左侧和右侧都不同）。在起源附近，有一个扰动区，可以从一个哈密顿量传递到另一个。本文的主要结果是随机均质化，因为过渡区的长度为零。更确切地说，在极限上，我们获得了两个确定性的右和左汉顿人，其起源有确定性的连接条件。该论文的主要困难和新颖性来自哈密顿族人不是静止的ergodic的事实。据我们所知，这是第一个指定的随机均质化结果。这项工作是由交通流量应用程序激励的。
We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered hamiltonian is closed to given stationary ergodic hamiltonians (which are different on the left and on the right). Near the origin, there is a perturbation zone which allows to pass from one hamiltonian to the other. The main result of this paper is a stochastic homogenization as the length of the transition zone goes to zero. More precisely, at the limit we get two deterministic right and left hamiltonians with a deterministic junction condition at the origin. The main difficulty and novelty of the paper come from the fact that the hamiltonian is not stationary ergodic. Up to our knowledge, this is the first specified stochastic homogenization result. This work is motivated by traffic flow applications.
