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In this paper we consider the porous medium flow through a corrugated channel where the viscosity of the fluid can significantly change with the pressure. Assuming the exponential dependence of the viscosity and drag coefficient on the pressure, we propose the higher-order approximation of the solution to the nonlinear boundary-value problem governing the flow. To accomplish that, we combine the concept of the transformed pressure with asymptotic techniques.

Modelling of the porous medium flow with pressure-dependent viscosity and drag coefficient