Abstract
We are concerned with a semilinear parabolic differential inequality posed in an exterior domain of R-N, N >= 3. Some blow-up and existence results are established for the considered problem. The novetly of this paper lies in considering a nontrivial Dirichlet boundary condition, which depends both on time and space. Indeed, to the best of our knowledge, in all articles which deal with the blow-up of solutions in exterior domains, the considered boundary condition is trivial or depends only on space.