| Abstrakt: |
Let d ∈ {1, 2, 3,...} and Ω ⊂ ℝd be open bounded with Lipschitz boundary. Consider the reaction-diffusion parabolic problem P { u t | x | 4 + Δ (| Δ u | m − 2 Δ u) = k (t) | u | p − 1 u (x , t) ∈ Ω × (0 , T) , u (x , t) = ∂ x j u (x , t) = 0 , (x , t) ∈ ∂ Ω × (0 , T) , j ∈ { 1 , ... , d } , u (x , 0) = u 0 (x) , x ∈ Ω , where T > 0, m ∈ [2, ∞), p ∈ (1, ∞) and 0 ≠ u 0 ∈ W 0 2 , m (Ω) ∩ L p + 1 (Ω). We investigate the upper and lower bounds on the blow-up time of a weak solution to (P). [ABSTRACT FROM AUTHOR] |
