In this article, we consider the nonautonomous modified Swift–Hohenberg equation on infinite lattices. We first show the existence of a pullback-\({{\mathcal {D}}}\) attractor of the process generated by this equation. Then, we establish the existence of a unique family of invariant Borel probability measures carried by the pullback attractor. Finally, we construct statistical solutions for this equation on infinite lattices.

中文翻译：

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非自治离散修正 Swift-Hohenberg 方程的不变测度和统计解

在本文中，我们考虑了无限格上的非自治修正 Swift-Hohenberg 方程。我们首先展示了这个方程产生的过程的回撤- \({{\mathcal {D}}}\)吸引子的存在。然后，我们建立了由回调吸引子携带的唯一的不变 Borel 概率测度族的存在。最后，我们在无限格子上为这个方程构造统计解。