论文标题
无限尺寸系统的Smoluchowski-kramer近似具有状态依赖性阻尼
A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping
论文作者
论文摘要
我们研究了Smoluchowski-kramers近似的有效性，该类别在$ \ mathbb {r}^n $的有界域中的一类方程的有效性受到状态依赖性阻尼和受到多重噪声的扰动。我们证明，在小质量中，溶液会收敛到随机的准抛物线方程的溶液，其中产生了噪声引起的额外漂移。
We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of $\mathbb{R}^n$ subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass limit the solution converges to the solution of a stochastic quasilinear parabolic equation where a noise-induced extra drift is created.
