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HHto the 3-dimensional stochastic wave equation
编辑:数学学院  时间:2014-06-24  点击数:

题 目: HH"older continuity of the solution to the 3-dimensional stochastic wave equation

报告人: 黄靖宇博士(美国University of Kansas数学系)

时 间: 2014年6月25日 上午9:30

地 点: 数学楼629教研室

摘要: In this paper, we study the stochastic wave equations in the spatial dimension 3 driven by a Gaussian noise which is white in time and correlated in space. Our main oncern is the sample path H"older continuity of the solution both in time variable and in space variables. The conditions are given either in terms of the mean H"older continuity of the covariance function or in terms of its spectral measure. Some examples of the covariance functions are proved to satisfy our conditions, which include the case of the work cite{dalang4}. In particular, we obtain the H"older continuity results for the solution of the stochastic wave equations driven by (space inhomogeneous) fractional Brownian noises. For this particular noise, the optimality of the obtained H"older exponents is also discussed.

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