Homogenization of the G-equation with incompressible random drift in two dimensions
Homogenization of the G-equation with incompressible random drift in two dimensions
复制标题
二维不可压缩随机漂移 G 方程的齐次化
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Novikov
中科院分区：
文献类型：
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作者：
J. Nolen;A. Novikov
研究了具有随机漂移的G-方程解的均匀化极限。该Hamilton-Jacobi方程是在薄火焰状态下湍流流体中火焰传播的模型。对于流体速度场是统计平稳和遍历的，我们证明了充分条件的均匀化举行的概率为1。这些条件表示在旅行时间的相关控制问题。当空间维数等于2和流体速度是发散自由的，我们验证了这些条件下的随机流函数的增长适当的假设。
We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is statistically stationary and ergodic, we prove sufficient conditions for homogenization to hold with probability one. These conditions are expressed in terms of travel times for the associated control problem. When the spatial dimension is equal to two and the fluid velocity is divergence-free, we verify that these conditions hold under suitable assumptions about the growth of the random stream function.