Abstract
We are concerned with nonexistence results for a class of systems of parabolic inequalities in (0, infinity) x A, where A = {x is an element of R-N : 1 < |x| <= 2}. The considered systems involve a singular potential function V (x) = (|x| - 1)(-rho), rho > 0, in front of the power nonlinearities. Two types of inhomogeneous boundary conditions on partial derivative B-2 = {x is an element of R-N : |x| = 2} are discussed: Neumann type conditions and Dirichlet type conditions. Using a unified approach, an optimal criterium of nonexistence is obtained for both cases. Our study yields naturally optimal nonexistence results for the corresponding stationary systems.
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