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

2024/06/21 by John Ivanhoe, Ivanhoe, John, Michael Salins +1
Mathematics · #60H15 #FOS: Mathematics #Numerical methods for differential equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2406.15672

openalex publication_date 2024/06/21 · openalex created_date 2024/06/27 · openalex updated_date 2026/07/28

Abstract

We examine stochastic reaction-diffusion equations of the form (∂ u)/(∂ t) = A u(t,x) + f(u(t,x)) + σ(u(t,x))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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