In this paper, we consider a certain class of second order nonlinear PDEs with damping and space-time white noise forcing, posed on the d -dimensional torus. This class includes the wave equation for $$d=1$$ d = 1 and the beam equation for $$d\le 3$$ d ≤ 3 . We show that the Gibbs measure is the unique invariant measure for this system. Since the flow does not satisfy the strong Feller property, we introduce a new technique for showing unique ergodicity. This approach may be also useful in situations in which finite-time blowup is possible.

中文翻译：

---

一类具有加性时空白噪声的随机双曲方程的唯一遍历性

在本文中，我们考虑了在 d 维圆环上构成的一类具有阻尼和时空白噪声强迫的二阶非线性偏微分方程。此类包括 $$d=1$$ d = 1 的波动方程和 $$d\le 3$$ d ≤ 3 的梁方程。我们表明吉布斯测度是该系统的唯一不变测度。由于流不满足强 Feller 性质，我们引入了一种新技术来显示独特的遍历性。这种方法在可能出现有限时间膨胀的情况下也很有用。