We prove a uniform large deviations principle for the law of the solutions to a class of Burgers-type stochastic partial differential equations in any space dimension. The equation has nonlinearities of polynomial growth of any order, the driving noise is a finite dimensional Wiener process, and the proof is based on variational principle methods. We prove the uniform large deviations principle for the law of the solutions in two different topologies. First, in the C([0, T] : L^ρ(D)) topology where the uniformity is over L^ρ(D)-bounded sets of initial conditions, and secondly in the \(C([0,T]\times \bar D)\) topology with uniformity being over bounded subsets in the \(C_{0}(\bar D)\) norm.

我们证明了一类任意空间维度上的Burgers型随机偏微分方程的解律的一致大偏差原理。该方程具有任意阶多项式增长的非线性，驱动噪声为有限维维纳过程，证明基于变分原理方法。我们证明了两种不同拓扑中解律的一致大偏差原理。首先，在C ([0, T ] : L ^ρ ( D )) 拓扑中，均匀性超过L ^ρ ( D ) 有界初始条件集，其次在\(C([0,T]\次 \bar D)\)在\(C_{0}(\bar D)\)范数中，具有均匀性的拓扑在有界子集上。