Gerencsér, M., & Hairer, M. (2022). Boundary renormalisation of SPDEs. Communications in Partial Differential Equations, 47(10), 2070–2123. https://doi.org/10.1080/03605302.2022.2109173
We consider the continuum parabolic Anderson model (PAM) and the dynamical Φ⁴ equation on the 3-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin boundary conditions gives rise to a divergent boundary renormalisation. Furthermore for Φ₃⁴ a ‘boundary triviality’ result is obtained: if one approximates the equation with Neumann boundary conditions and the usual bulk renormalisation, then the limiting process coincides with the one obtained using Dirichlet boundary conditions.
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Project title:
Regularisierung durch Rauschen: Diskrete und stetige Systeme: P34992-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
