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Scaling limits and stochastic homogenization for some nonlinear parabolic equations. (English) Zbl 1479.35058

Summary: The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns requiring the existence of a space-time stationary eternal solution of a stochastically perturbed heat equation, the problem transforms to the qualitative homogenization of a uniformly elliptic, space-time stationary, divergence form, nonlinear partial differential equation, the study of which is the second aim of the paper. An important step is the construction of correctors with the appropriate behavior at infinity.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K15 Initial value problems for second-order parabolic equations
35K59 Quasilinear parabolic equations
35R60 PDEs with randomness, stochastic partial differential equations
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