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We examine stochastic reaction-diffusion equations of the form ∂ u/∂ t = A u(t,x) + f(u(t,x)) + σ(u(t,x))Ẇ(t,x) and provide sufficient conditions on the reaction term and multiplicative noise term that guarantees solutions never explode in finite time.
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Ivanhoe et al. (2024) studied this question.
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