Scaling limits and stochastic homogenization for some nonlinear parabolic equations

Cardaliaguet, Pierre, Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367 and Souganidis, Panagiotis E. 2022. Scaling limits and stochastic homogenization for some nonlinear parabolic equations. Journal of Differential Equations 307 , pp. 389-443. 10.1016/j.jde.2021.10.057

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0022-0396
Funders:	Royal Society, EPSRC
Date of First Compliant Deposit:	8 December 2021
Date of Acceptance:	27 October 2021
Last Modified:	23 Nov 2024 03:30
URI:	https://orca.cardiff.ac.uk/id/eprint/145669

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