论文标题
Smoluchowski-kramers在二维的奇异随机波方程的近似
Smoluchowski-Kramers approximation for singular stochastic wave equations in two dimensions
论文作者
论文摘要
我们研究了由参数$ε> 0 $索引的非线性阻尼波方程的家族，并由两维曲线上的时空白噪声强迫，具有多项式和正弦非线性。我们表明，作为$ε\至0 $，这些方程的解决方案会收敛到相应的二维随机量化方程的解。在正弦的非线性情况下，在任意大时期证明了收敛性，而在多项式情况下，我们证明，即使参数$ε$也无法在相应的波方程中参数$ε$变为零，即使参数$ε$也将其变为零。
We study a family of nonlinear damped wave equations indexed by a parameter $ε>0$ and forced by a space-time white noise on the two dimensional torus, with polynomial and sine nonlinearities. We show that as $ε\to 0$, the solutions to these equations converge to the solution of the corresponding two dimensional stochastic quantization equation. In the sine nonlinearity case, the convergence is proven over arbitrary large times, while in the polynomial case, we prove that this approximation result holds over arbitrary large times when the parameter $ε$ goes to zero even with a lack of suitable global well-posedness theory for the corresponding wave equations.
