Preventing Finite-Time Blowup in a Constrained Potential for Reaction-Diffusion Equations

Published 21 Jun 2024 in math.PR | (2406.15672v2)

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

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