In this paper, a porous medium equation with local source and nonlocal boundary condition is studied. By using the fixed point theorem and comparison principle. The global existence and blow-up of solutions are obtained .
In this paper, a porous medium equation with nonlocal boundary condition and a localized source is considered. The existence and blow-up properties of solutions are obtained under some conditions.
This work is concerned with an initial boundary value problem for a nonlocal porous medium equation with inner absorption and weighted nonlocal boundary condition. We obtain the roles of weight function on whether determining the blowup of nonnegative solutions or not and establish the precise blow-up rate estimates under some suitable condition.
Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition