Scaling limits and stochastic homogenization for some nonlinear parabolic equations

Pierre Cardaliaguet (1) , Nicolas Dirr (2) , Panagiotis E. Souganidis (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics [Cardiff]
3 Department of Mathematics [Chicago]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Cardaliaguet, Nicolas Dirr, Panagiotis E. Souganidis. Scaling limits and stochastic homogenization for some nonlinear parabolic equations. Journal of Differential Equations, 2022, 307, pp.389-443. ⟨hal-02536024⟩