... we have used the facts that fx, ·/≡ 0 for any x ∈ ∂Ω and w1y, t1 > 0 for any y ∈ Ω, which is a direct result of the previous case.Therefore, the claim is true and thus t1 T, ... 1andΩgx, ydy ≤ 1 for any x ∈ ∂Ω in Lemma 2.2, we canobtain w1,w2 ≥ 0, 0 in QTunder the assumption that w1x, 0,w2x, 0 ≥ 0, 0 for x ∈ Ω.Indeed, for any >0, we can ... parabolic system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 8, pp. 2406–2416, 2008.23 P. Souplet, “Uniform blow-up profiles and boundary behavior for diffusion equations...