کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4610300 | 1338555 | 2015 | 50 صفحه PDF | دانلود رایگان |
We study homogenization for fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media from the qualitative and quantitative perspectives. Under suitable hypotheses, solutions to fully nonlinear uniformly parabolic equations in spatio-temporal media homogenize almost surely. In addition, we obtain a logarithmic rate of convergence for this homogenization in measure, assuming that the environment is strongly mixing with a prescribed logarithmic rate. A general methodology to study the stochastic homogenization and rates of convergence for stochastic homogenization of uniformly elliptic equations was introduced by Caffarelli, Souganidis, and Wang [1], and Caffarelli and Souganidis [2]. We extend their approach to fully nonlinear uniformly parabolic equations, developing a number of new arguments to handle the parabolic structure of the problem.
Journal: Journal of Differential Equations - Volume 258, Issue 3, 1 February 2015, Pages 796–845