On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field

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• 作者：Sandra Cerrai^a ; ^{cerrai@math.umd.edu} ; Michael Salins^b
• 关键词：Stochastic partial differential equations ; Smoluchowski&ndash ; Kramers approximation ; Magnetic field ; Small mass asymptotics
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：273-303
• 全文大小：375 K
• 卷排序：127

文摘

We study the validity of the so-called Smoluchowski–Kramers approximation for a two dimensional system of stochastic partial differential equations, subject to a constant magnetic field. Since the small mass limit does not yield to the solution of the corresponding first order system, we regularize our problem by adding a small friction. We show that in this case the Smoluchowski–Kramers approximation holds. We also give a justification of the regularization, by showing that the regularized problems provide a good approximation to the original ones.