In the present paper, we obtain a new a priori estimate of the solution
of the initial-boundary value Problem for the Porous medium
equation with non-linear source. Also, we present the conditions
guaranteeing the existence of a global classical solution of this Problem
as well as the cases for which the solution may blow up (the last
is discussed in [1,2]). We have to establish an a priori estimate of the
already studied heat type problem with Dirichlet conditions instead
(see [3]). The main tool which is going to be utilized for finding an a
priori estimate and constructing an upper bound for the solution, is
the maximum principle
(EN)
University of Crete
