论文标题
噪声对MEMS技术中某些模型的淬火的影响
Impacts of noise on quenching of some models arising in MEMS technology
论文作者
论文摘要
在当前的工作中，我们研究一个随机抛物面问题。实际上，在控制设备的电势差的随机波动的情况下，理想化的电动电动机（微电动机械系统）设备的研究实际上是由潜在的问题进行的。 我们首先介绍数学模型，然后推断出一些局部存在结果。接下来，对于模型的某些特定版本，关于其边界条件，我们得出了淬灭结果以及对这种奇异性发生的概率的估计。在一个维度上对问题的其他数值研究随后遵循，就其淬灭行为进一步研究了该问题。
In the current work we study a stochastic parabolic problem. The underlying problem is actually motivated by the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference controlling the device. We first present the mathematical model and then we deduce some local existence results. Next for some particular versions of the model, regarding its boundary conditions, we derive quenching results as well as estimations of the probability for such singularity to occur. Additional numerical study of the problem in one dimension follows, investigating the problem further with respect to its quenching behaviour.
