论文标题
随机反应扩散方程中瞬时模式的准erer剂
Quasi-Ergodicity of Transient Patterns in Stochastic Reaction-Diffusion Equations
论文作者
论文摘要
我们研究了使用准平台和准凝胶措施的框架在SPDE中出现的瞬态模式。特别是，我们证明了一类被添加剂圆柱噪声扰动的反应扩散系统的准平台和准凝胶量度的存在和独特性。我们获得了$ l^2 $的收敛结果，几乎可以肯定，并以$ l^2 $ norm的指数融合了准平台措施的指数率。这些结果使我们能够定性地表征这些系统在相应的确定性系统不变的歧管的社区中的行为，在某些时间很大程度上$ t> 0 $，条件是剩下的时间$ t $。我们在这里采用的方法是基于光谱差距条件，并且不仅限于小噪声状态。
We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of reaction-diffusion systems perturbed by additive cylindrical noise. We obtain convergence results in $L^2$ and almost surely, and demonstrate an exponential rate of convergence to the quasi-stationary measure in an $L^2$ norm. These results allow us to qualitatively characterize the behaviour of these systems in neighbourhoods of an invariant manifold of the corresponding deterministic systems at some large time $t>0$, conditioned on remaining in the neighbourhood up to time $t$. The approach we take here is based on spectral gap conditions, and is not restricted to the small noise regime.
