Mild solutions explode with positive probability when β ∈ (1,3) and γ ∈ (β/2, (β+3)/4), or when γ ≤ β/2, for the stochastic heat equation on the periodic interval with space-time white noise.
In stantaneous everywhere-blowup of parabolic SPDEs
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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 γ ≤ β/2, for the stochastic heat equation on the periodic interval with space-time white noise.