• Le Chen
• Auburn University
• Date: Aug. 23, Tuesday, 2022
• Time: 2:30pm -- 3:30pm
• Room: Parker 326
• Abstract: The following one-dimensional stochastic wave equation has been studied as early as in the Walsh's notes 1980's:

\begin{align*} \partial_t^2 u(t,x) = \Delta u(t,x) + \lambda u(t,x) \dot{W}(t,x) \end{align*} where \(\dot{W}(t,x)\) refers to the space-time white noise and \(\lambda\ne 0\) is a constant. The upper bound for the moment Lyapunov exponents are known in the literature:

\( \displaystyle \limsup_{t\to\infty} t^{-1} \log \mathbb{E} \left[ u(t,x)^p \right] \le C p^{3/2},\quad p\ge 2.\) In this talk, I will present a recent joint-work with Yuhui Guo and Jian Song arXiv:2206.10069 where we proved the corresponding lower bounds: \(\displaystyle \liminf_{t\to\infty} t^{-1} \log \mathbb{E} \left[ u(t,x)^p \right] \ge C p^{3/2},\quad p\ge 2.\)