论文标题
随机波方程与耗散阻尼的多项式混合
Polynomial mixing of a stochastic wave equation with dissipative damping
论文作者
论文摘要
我们研究了一类半线性波方程的长期统计数据，该方程对悬浮在连续培养基中的粒子运动的运动进行了建模，同时通过加性高斯噪声受到随机扰动的影响。通过与非线性反应设置相比，已知溶液具有几何牙齿性，我们发现，在非线性耗散阻尼的影响下，混合速率至少是任何阶的多项式。这依赖于Lyapunov条件的结合，Markov Transition Semigroup的缔约财产以及$ D $ - 小型套件的概念。
We study the long time statistics of a class of semi--linear wave equations modeling the motions of a particle suspended in continuous media while being subjected to random perturbations via an additive Gaussian noise. By comparison with the nonlinear reaction settings, of which the solutions are known to possess geometric ergodicity, we find that, under the impact of nonlinear dissipative damping, the mixing rate is at least polynomial of any order. This relies on a combination of Lyapunov conditions, the contracting property of the Markov transition semigroup as well as the notion of $d$--small sets.
