隨機熱傳導方程式之研究;A Study on Stochastic Heat Equations

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题名:	隨機熱傳導方程式之研究;A Study on Stochastic Heat Equations
作者:	須上苑
贡献者:	國立中央大學數學系
关键词:	數學
日期:	2012-12-01
上传时间:	2014-03-17 14:20:57 (UTC+8)
出版者:	行政院國家科學委員會
摘要:	研究期間：10111~10207;There are two common approaches to stochastic partial differential equations.One is infinitely dimensional approach, the other one invented by J. Walsh is more probabilistic. We are using Walsh’s approach and consider stochastic heat equations (SHEs) which is a family of heat equations with added Gaussian noises. Since rough noises have been added, the behaviors of solutions are different from the [deterministic] heat equations (HEs). For example, in dimension one with constant initial data, the solutions to SHEs have fluctuations. Our plan is to understand the behaviors of the solutions, such as intermittency, fractal-like exceedance sets. Moreover, by observation of the solutions in mild form, intuitively the solutions can be locally approximated by the solutions to stochastic differential equations. We are interested in giving a rigorous proof of it. When the initial data vanishes at infinity, the solutions to HEs go to infinity exponentially; in the case of SHEs, we like to know how fast the solutions to SHEs dissipate.
關聯:	財團法人國家實驗研究院科技政策研究與資訊中心
显示于类别:	[數學系] 研究計畫

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