The authors study blow-up and global existence for the system of porous medium equations
coupled through the nonlinear boundary conditions
The initial data , are assumed to be continuous nonnegative and compactly supported, , . It is shown that all solutions of this problem exist globally if and only if . In the blow-up case, the authors find necessary and sufficient conditions in terms of for blow-up of all nontrivial solutions. They also establish the blow-up rate of blowing up solutions which are increasing in time, and they characterize the blow-up sets , of solutions satisfying the blow-up rate mentioned above. Each of , is either , a bounded interval containing 0 or the interval and any combination of these alternatives is possible.