BLOW-UP PHENOMENA IN SOME POROUS MEDIUM PROBLEMS

We consider a Dirichlet type initial-boundary value problem for the porous medium equation with a power function reaction term. We determine a condition on the initial data which ensures blow-up of the solution in finite time and an upper bound for the blow-up time. We also discuss when blow-up does not occur and a more general initial-boundary value problem where blow-up does occur.