具乘性噪声的非局部随机Swift-Hohenberg方程随机吸引子的上半连续性及不变测度的存在性

The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation

We consider the impact of additive Gaussian white noise on a supercritical pitchfork bifurcation in an unbounded domain. As an example we focus on the stochastic Swift-Hohenberg equation with polynomial nonlinearity. Here we identify the order where small noise first impacts the bifurcation. Using an approximation via modulation equations, we provide a tool to analyse how the noise influences the dynamics close to a change of stability.

随机约束修正Swift-Hohenberg方程的鞅解

Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation

本文利用能量估计、紧性准则和Skorokhod定理的推广，在Hilbert空间框架下证明了Stratonovich乘性噪声驱动的随机约束修正Swift-Hohenberg方程全局鞅解的存在性。

Hilbert流形上随机约束修正Swift-Hohenberg方程的全局解与不变性

On the Global solution and Invariance of stochastic constrained Modified Swift-Hohenberg Equation on a Hilbert manifold

本文研究了Hilbert流形上随机约束修正Swift-Hohenberg方程的随机推广，利用Khashminskii非爆炸测试证明了其全局适定性与子流形不变性。

Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation

In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-Hohenberg equation adding an additive noise. We prove the existence of a global solution of that equation on the two dimensional torus. In addition, inserting a scaling parameter, we consider the equation on a large domain near its change of stability. We observe numerically that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic G…

随机修正Swift-Hohenberg方程的整体鞅与逐路径解及不变测度的无穷正则性

Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift-Hohenberg equation

研究带乘性噪声的2D随机修正Swift-Hohenberg方程，证明了整体鞅解与逐路径解的存在性，并据此建立马尔可夫半群，最终证明了不变测度的存在性及其无穷正则性。

L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence

Generalizing the L-Kuramoto-Sivashinsky (L-KS) kernel from our earlier work, we give a novel explicit-kernel formulation useful for a large class of fourth order deterministic, stochastic, linear, and nonlinear PDEs in multispatial dimensions. These include pattern formation equations like the Swift-Hohenberg and many other prominent and new PDEs. We first establish existence, uniqueness, and sharp dimension-dependent spatio-temporal Hölder regularity for the canonical (zero drift) L-KS SPDE, driven by white noise on $\{\Rp\times\Rd\}_{d=1}^{3}$. The spatio-temporal Hölder exponents are exactl…