In this study we give a mathematical formulation of the phenomenon of groundwater pollution which is due to a non-Darcy flow in an unsaturated zone and in the presence of solute transport and of heat transfer. The model obtained is a system of coupled partial nonlinear equations of evolution type. The principal aim of this investigation is to treat theoretically the system obtained (existence of solution), within an appropriate functional framework. Thus, we give the necessary mathematical conditions to be verified by the system's data.
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