research article
Periodic space-time homogenisation of the φ24 equation
March 1, 2025
We consider the homogenisation problem for the φ42 equation on the torus T2, namely the behaviour as ε →0 of the solutions to the equation suggestivelywritten as ∂tuε − ∇ · A(x/ε, t/ε2)∇uε = −u3ε + ξ where ξ denotes space-time white noise and A :T2×R is uniformly elliptic, periodic and Hölder continuous. When the noise is regularised at scale δ << 1 we show that any joint limit ε, δ→0 recovers the classical dynamical φ42 model. In certain regimes or if the regularisation is chosen in a specific way adapted to the problem, we show that the counterterms can be chosen as explicit local functions of A.
Type
research article
Web of Science ID
WOS:001375441500001
Author(s)
EPFL
Singh, Harprit
University of Edinburgh
Date Issued
2025-03-01
Publisher
Published in
Volume
288
Issue
5
Article Number
110762
Editorial or Peer reviewed
REVIEWED
Written at
EPFL
EPFL units
Available on Infoscience
December 24, 2024
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