A priori bounds for the generalized parabolic Anderson model in the full subcritical regime
Year: 2026
Type: preprint
Abstract: We show a priori bounds for the generalized Parabolic Anderson Model $(\partial_t - Δ)u = σ(u) \diamond ξ$ in finite volume in the full subcritical regime. The approach is based on the observation that, for constant initial data, the time interval over which the solution remains close to its initial condition can be chosen uniformly in the value of the initial condition. A comparison principle is then used to extend this estimate to general bounded initial data.
Source: arXiv (Cornell University)
Authors: Esquivel, Salvador, Schwarzfischer, Felix
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204184478