Mild solutions explode with positive probability when β ∈ (1,3) and γ ∈ (β/2, (β+3)/4), or when β > 1 and γ ∈ (0, β/2].
Nonexplosion for a large class o f superlinear stochas- tic parabolic equations, in arbitrary spatial dimension
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Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise
Mild solutions explode with positive probability when β ∈ (1,3) and γ ∈ (β/2, (β+3)/4), or when β > 1 and γ ∈ (0, β/2].