Existence Of Weak Solution For Single-Phase Flow In Porous Media With Variable Coefficients

Fluid mechanics is a discipline that studies the laws of motion of fluid mechanics and its applications.In traditional fluid mechanics,the results of the single-phase flow model in porous media are mostly concentrated in the case where the relevant parameters of the porous media are constants and constant functions.However,in the actual process of flow in porous media,the relevant parameters of porous media change dynamically.Therefore,in order to more accurately describe the actual phenomenon concerning flow in porous media,it is necessary to study the single-phase flow model with variable coefficient in porous media.In this paper,a modified single-phase flow model in porous media with variable coefficients is established by dealing with the nonlinear relationship between permeability and porosity,and the existence of weak solutions of this model is demonstrated by using viscous methods and energy methods.The main contents and research results are as follows:Firstly,for the mass equation in the modified single-phase flow model in porous media with variable coefficients,we use it as the basic equation to deduce the Dirichlet model of the quasi-parabolic equation which is equivalent to the original equation;Secondly,the approximation system of the quasi-parabolic equation Dirichlet problem is constructed by the viscousity method,and the existence of the viscousity solution of the problem is proved by the method of upper and lower solutions.Finally,we show that the viscousity solution of the quasi-parabolic equation obtained by the energy method is the weak solution,which proves the existence of the weak solution of the single-phase flow equation in porous media with variable coefficients and provides a mathematical theoretical basis for solving porous flow problem in real life.