摘  要:

Homogenization is a general phenomenon when physical processes in periodic or random environments exhibit homogeneous long time dynamics due to large space averaging of the variations in the environment.  While this area of Mathematics saw a slew of remarkable developments in the last 20 years, the progress in the case of reaction-diffusion equations, which model many important physical phenomena, has been somewhat limited due to the homogenized dynamic involving discontinuous solutions to different (first-order) equations.  
In this talk I will discuss the first proofs of homogenization for reaction-diffusion equations with random not necessarily isotropic reactions in several spatial dimensions. These include the cases of both time-independent and time-dependent reactions, with the later proof employing a new subadditive ergodic theorem for time-dependent environments. We obtain analogous results for G-equations with random flame speeds and incompressible background advections.
This talk is based on joint works with Andrej Zlatoš.