UC Irvine

This dissertation considers the random homogenization of coercive Hamilton-Jacobi equations and it gives the most generalized result in 1-D. Basically, we can prove that in the stationary ergodic media, the random homogenization holds as long as the Hamiltonian is coercive. This is an extension of the result by Armstrong, Tran and Yu when the Hamiltonain is separable. We also provide some application of random homogenizaton in front propagation based on the analysis of inviscid G-equation model, it is proved that with 2-d random shear flows, the strain effect reduces the propagation of the flame front.