ABSTRACT Let d ∈ {1, 2, 3, . . .} and Ω ⊂ ℝ d 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 ) $0 \ne u_0 \in W^{2,m}_0(\Omega) \cap L^{p+1}(\Omega)$ . We investigate the upper and lower bounds on the blow-up time of a weak solution to (P).