(untitled) (Journal of Partial Differential Equations, 2022)
In the paper, the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied. By constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem, the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained. The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundary conditions.