Modeling Mass Transport in Aquifers: The Distributed SourceProblem

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This is an award to support research on modeling of the movement of groundwater pollutants. The specific objective of this project is to devise a methodology for prediction of the movement of a specific, principal contaminant regardless of its stochastic properties, concentration or location in the mathematical model. Additionally, the investigator is considering sources of uncertainty relative to contaminant migration beyond those attributable to aquifer conductivity. He is exploring new foundations in functional-analytic theory (stochastic evolution equations, semigroups of operators, stochastic differential equations in Hilbert space) blended with some results on the classical heat flow equation in order to obtain new solutions of the advective dispersive transport equation in porous media subject to a general stochastic disturbance. The project is expected to produce a new systematic and general modeling procedure by which the stochastic properties of the concentration process can be predicted based on the stochastic properties of the disturbing stochastic process(es) at the boundary conditions, the source terms and/or the parameters. Additionally, it is expected that the variances of the processes will not be restricted to small magnitudes as it is the case with conventional perturbation techniques.