Establishes non-explosion for superlinear stochastic parabolic PDEs with space-time colored noise in arbitrary dimensions under Neumann, periodic or Dirichlet conditions, achieving χ up to 1 + (1-η)/(2β).
Stochastic Equations in Infinite Dimensions
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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.
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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.