论文标题
与缺陷的某些周期性汉密尔顿 - 雅各比方程的均质化
Homogenization of some periodic Hamilton-Jacobi equations with defects
论文作者
论文摘要
我们研究了一类汉密尔顿 - 雅各比方程的均质化，其中通过在起源附近扰动本来是周期性的哈密顿量来获得的哈密顿量。我们证明，限制问题由原点以外的汉密尔顿 - 雅各比方程组成，其有效的汉密尔顿人与定期均质化相同，在起源时以有效的污染条件补充，可以跟踪扰动。讨论了各种评论和扩展。
We study homogenization for a class of stationnary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.
