Abstract
We establish new blow-up results for a higher order (in time) evolution inequality involving a convection term in an exterior domain of RN. We study two types of inhomogeneous boundary conditions: Dirichlet and Neumann. Using a unified approach, we obtain optimal criteria of Fujita type for each case. Our study yields naturally optimal nonexistence results for the corresponding stationary problems. We also investigate the effect of a nonlinear memory term on the critical behaviors of the considered problems. Notice that no restriction on the sign of solutions is imposed.
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