论文标题
具有记忆的非线性随机反应扩散方程的刻薄性
Ergodicity of a nonlinear stochastic reaction-diffusion equation with memory
论文作者
论文摘要
我们考虑具有记忆项，多项式非线性和随机扰动的一类半线性差异方程。对于广泛的非线性，我们研究了系统的统计稳态状态，并发现它们具有与弱解决方案兼容的规律性。此外，如果相位空间中有足够多的方向被随机强迫，我们采用\ emph {广义耦合}方法来确定系统对系统具有成倍有吸引力的不变概率度量的存在和独特性。这扩展了先前在[Bonaccorsi等，Siam J. Math。肛门，44（2012）]。
We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For a broad class of nonlinearities, we study statistically steady states of the system and find that they possess regularities compatible with those of the weak solutions. Moreover, if sufficiently many directions in the phase space are stochastically forced, we employ the \emph{generalized coupling} approach to establish the existence and uniqueness of the invariant probability measure to which the system is exponentially attractive. This extends ergodicity results previously established in [Bonaccorsi et al., SIAM J. Math. Anal., 44 (2012)].
