Abstract: In order to describe the reaction diffusion problems of three media in physics, such as mechanics of porous media, fluid mechanics, gas flow and so on, the asymptotic behavior of a class of parabolic equations of porous media,with 3 variables coupled with a weighted nonlocal boundary and a nonlinear internal source is studied.The upper and lower solutions of the first eigenvalue are broken, and the upper and lower solutions of the equations are constructed by using the ordinary differential equation method, and the comparison theorem is quoted. It is proved that the whole existence of the solution of the parabolic equations of porous media with the power function and the exponential function fully coupled and the sufficient conditions for the solution in the finite time blasting are obtained.On the basis of the existing results, provide more theoretical support for porous media and fluid mechanics are achieved.

Key words: porous media parabolic equations, the comparison principle, global solution, blow up