This paper aims at studying the boundary value for second order quasilinear elliptic equations with nonlinear boundary condition in exterior domain.

In this paper, we prove the existence and uniqueness of global weak solution of non Newton Filtration equation with a kind of nonlinear boundary condition.

This dissertation is to discuss the laws of fluids in porous medium for original boundary value problem of some quasi-linear parabolic equations with the third type nonlinear boundary condition.