document: Mathematical modelling of the work of the system of wells in a layer with the exponential law of permeability variation and the mobile liquid interface We construct and study a two-dimensional model of the work of the system of wells in a layer with the mobile boundary between liquids of various viscosity . We use a ` plunger ' displacement model of liquids . The boundaries of the filtration region of these liquids are modelled by curves of the Lyapunov class . Unlike familiar work , we solve two-dimensonal problems in an inhomogeneous layer when the mobile boundary and the boundaries of the filtration region are modelled by curves of the Lyapunov class . We show the practical convergence of the numerical solution of the problems studied
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