A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton-Jacobi Equations
A New Approximation for Effective Hamiltonians for Homogenization of a class of Hamilton-Jacobi Equations
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一类哈密顿-雅可比方程齐次化的有效哈密顿量的新近似
DOI：
10.1137/100799885
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Hongkai Zhao
中科院分区：
文献类型：
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作者：
S. Luo;Yifeng Yu;Hongkai Zhao
我们提出了一个新的公式来计算一类Hamilton-Jacobi方程的均匀化有效哈密顿量。我们的公式利用了巴伦和詹森的观察[Comm.偏微分方程，15（1990），pp. 1713-1742]关于Hamilton-Jacobi方程的粘性上解。其关键思想是将有效哈密顿量与一个合适的有效方程联系起来。我们的公式的主要优点是，只有一个辅助方程需要解决，以计算有效的哈密顿量H <$（p）的所有p。误差估计和稳定性证明，并给出数值例子来证明的性能。
We propose a new formulation to compute effective Hamiltonians for homogenization of a class of Hamilton–Jacobi equations. Our formulation utilizes an observation made by Barron and Jensen [Comm. Partial Differential Equations, 15 (1990), pp. 1713–1742] about viscosity supersolutions of Hamilton–Jacobi equations. The key idea is to link the effective Hamiltonian to a suitable effective equation. The main advantage of our formulation is that only one auxiliary equation needs to be solved in order to compute the effective Hamiltonian H¯(p) for all p. Error estimates and stability are proved and numerical examples are presented to demonstrate the performance.