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).
Global solutions to the stochastic reaction-diffu sion equation with su- perlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain
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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].
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Nonexplosion for a large class of superlinear stochastic parabolic equations, in arbitrary spatial dimension
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).
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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].