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A filtration model with the generalized Darcy’s law making allowance for nonlocal and nonlinear effects has been developed. The expression for the law was derived within the relaxation formalizm of nonequilibrium thermodynamics. The developed model is applied to analyze the influence of relaxation effects on the phase velocity of small wave-like perturbations. The character of nonlinear traveling waves is determined. The properties of polynomial and self-similar solutions are analyzed.

Solutions of the Model of Liquid and Gas Filtration in the Elastic Mode with Dynamic Filtration Law