On blow-up results for solutions of inhomogeneous evolution equations and inequalities

The main purpose of this work is to obtain blow-up results for solutions of the inequality |u|t Δ |u|σ u + |u|q + ω(x) on the half-space R1 + × Rn, where n 1, σ 0, q > 1 + σ, and ω:Rn → [0,+∞) is a nontrivial locally integrable function, and, in particular, to establish that forn>2 the critical blow-up exponent q∗ = n(1+ σ)/(n− 2) belongs to the blow-up case.  2003 Elsevier Inc. All rights reserved