Abstract
We provide sufficient conditions for the nonexistence of global positive solutions to the nonlocal evolution equation u(tt)(x, t) = (J * u - u)(x, t) + u(p)(x, t), (x, t) is an element of R-N x (0, infinity), (u(x, 0), u(t)(x, 0)) = (u(0)(x), u(1)(x), x is an element of R-N, where J : R-N -> R+, p > 1, and u(0), u(1)) is an element of L-loc(l) (R-N; R+) x L-loc(l) (R-N; R+). Next, we deal with global nonexistence for certain nonlocal evolution systems. Our method of proof is based on a duality argument.