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Preventing Finite-Time Blowup in a Constrained Potential for Reaction-Diffusion Equations
John Ivanhoe, Michael Salins · 2024-06-22 · via math.PR updates on arXiv.org

We examine stochastic reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{A} u(t,x) + f(u(t,x)) + σ(u(t,x))\dot{W}(t,x)$ and provide sufficient conditions on the reaction term and multiplicative noise term that guarantees solutions never explode in finite time.

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