(untitled) (Journal of Partial Differential Equations, 2009)
In this note we study the nonexistence of nontrivial global solutions on S=R^N×(0,∞) for the following inequalities: |u|_t≥Δ(|u|^m-1u)+|u|^q, and |u|_t≥div(|∇u|^p-2∇|u|)+|u|^q. When m, p, q satisfy some given conditions, the nonexistence of nontrivial global solution is proved, without taking their traces on the hyperplans t=0 into account.