全次临界区域内广义抛物Anderson模型的先验界
A priori bounds for the generalized parabolic Anderson model in the full subcritical regime
AI总结：
该研究利用正则性结构框架，证明了有限体积下广义抛物Anderson模型在全次临界区域内的先验界，为该模型的分析提供了关键的理论支撑。
AI中文摘要：
我们利用正则性结构（regularity structures）框架，证明了有限体积下广义抛物Anderson模型（$(\u2202_t - \u0394)u = \u03c3(u) \u25c7 \u03be$）在全次临界区域内的先验界。该方法基于如下观察：对于常数初始数据，其保证存在时间与数据大小无关；随后通过特定的非线性变换，为辅助场$v$构建了一个纯传输型偏微分方程，且$v$始终保持与$u$的均匀接近。特别地，该方法未引入局部理论表述中不存在的额外代数论证。
英文摘要：
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.
