Under some conditions, a blowup result is proved for the solution u of: \[{gathered} u_t = Δ u - | {∇ u} |^q + | {u} |p - 1 u, t > 0, x ∈ Ω \\ u(t,x) = 0, t > 0, x ∈ Γ , \\ u(0,x) = φ (x), x ∈ Ω . \\ {gathered} \] The associated elliptic problem is also studied.
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Chipot et al. (1989) studied this question.
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