期刊
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
卷 46, 期 1, 页码 165-199出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2020.1831020
关键词
Homogenization; mixing; stochastic Hamilton-Jacobi equations; scaling limits; pathwise viscosity solutions
资金
- National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship [DMS-1902658]
This study focuses on the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. The results show that the homogenized equations are stochastic Hamilton-Jacobi equations with deterministic, spatially homogenous Hamiltonians driven by white noise in time. Additionally, the paper proves some general regularity and path stability results for stochastic Hamilton-Jacobi equations, which are essential for proving homogenization results and are of independent interest.
We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized equations are stochastic Hamilton-Jacobi equations with deterministic, spatially homogenous Hamiltonians driven by white noise in time. The paper also contains proofs of some general regularity and path stability results for stochastic Hamilton-Jacobi equations, which are needed to prove some of the homogenization results and are of independent interest.
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