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Paper presents a numerical method for solving the initial boundary-value problem for a certain quasilinear parabolic equation describing the low velocity filtration problem. The convergence of the method is proved.
The paper discusses the physical basis of the process of filtration of water in a case of very low velocities and presents the mathematical model of the process, based on a new constitutive formula. The existence and uniqueness of a weak solution to the resulting nonhomogeneous initial boundary-value problem is then proven.
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