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- W1985264352 abstract "Following the theory presented in Part I and Part II of these series of articles, functional analysis theory and a formulation of the Ito's lemma in Hilbert spaces are outlined as a practical alternative to the problem of finding the equations satisfying the moments of a stochastic partial differential equation of the type appearing in groundwater flow. By combining the moments equations derived from Ito's lemma and the strongly continuous semigroup associated with a particular partial differential operator in a Sobolev space, very simple solutions of the moments equations can be obtained. The most important feature of the moments equations derived from Ito's lemma is that these deterministic equations can be solved by any analytical or numerical method available in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method provides a rigorous bridge between the abstract-theoretical analysis of stochastic partial differential equations and computer-oriented numerical techniques. An illustrative example showed the potential applications of the method in regional groundwater flow analysis subject to general white noise disturbances. The example used the present method in combination with the boundary integral equation method to solve the problem of regional groundwater flow in a two-dimensional domain subject to a random phreatic surface. Given the stochastic properties of the boundary condition, the first two moments of the potential as well as sample functions were found." @default.
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- W1985264352 date "1985-12-01" @default.
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- W1985264352 title "Analysis of stochastic groundwater flow problems. Part III: Approximate solution of stochastic partial differential equations" @default.
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- W1985264352 doi "https://doi.org/10.1016/0022-1694(85)90022-8" @default.
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