It is mainly studied that the existence of weak solutions of single-phase flow equations in porous media with variable coefficients. Firstly, the Dirichlet problem of the quasilinear parabolic equation which is equivalent to the original equation is established. Then， the viscosity method is used to construct its approximation equation, and the existence of the viscosity solution of the quasilinear parabolic equation is proved by the methods of upper and lower solutions. Finally, it is shown that the viscous solution of the quasilinear 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.

porous media equation; single-phase flow; viscosity solutions; weak solution