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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  ju  (  x  ,  t  )  =  0  ,(  x  ,  t  )  ∈  ∂  Ω  ×  (  0  ,  T  )  ,     j  ∈  {  1  ,  …  ,  d  }  ,u  (  x  ,  0  )  =   u  0   (  x  )  ,x  ∈  Ω  ,where  T  &gt; 0,  m  ∈ [2, ∞),  p  ∈ (1, ∞) and0  ≠   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 ).

Bounds on Blow-Up Time for a Higher-Order Non-Newtonian Filtration Equation