主要研究变系数多孔介质单相流方程弱解的存在性。首先建立与原方程等价的拟抛物方程的Dirichlet问题, 然后利用粘性法构造其逼近方程, 并通过上下解方法证明拟抛物方程粘性解的存在性, 最后利用能量方法得到拟抛物方程的粘性解是其弱解, 证明了变系数多孔介质单相流方程弱解的存在性。

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.