Semigroup solutions to stochastic unsteady groundwater flow subject to random parameters |
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Authors: | S E Serrano T E Unny |
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Institution: | (1) Dept. of Civil Engineering, University of Kentucky, 40506-0046 Lexington, KY, USA;(2) Dept. of Systems Design Engineering, University of Waterloo, N2L 3G1, Ontario, Canada |
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Abstract: | Two methods for the solution of partial differential equations (PDE) for the general case of random in time physical parameters are presented and their application to the solution of unsteady regional groundwater flow equations are illustrated. The first method is the semigroup approach which directly offers a solution without resorting to closure approximations (hierarchy techniques), perturbation techniques, or Montecarlo simulation techniques. The semigroup approach can also handle the general stochastic problem when randomness also appears as initial conditions, boundary conditions or forcing terms. The second method is an approximation scheme to obtain the semigroup solution in complex cases and permits the solution of equations with more than one random coefficient. |
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Keywords: | Stochastic groundwater flow semigroups random in time Gaussian process random physical parameters stochastic partial differential equations |
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