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Preventing finite-time blowup in a constrained potential for reaction–diffusion equations

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  • Ivanhoe, John
  • Salins, Michael

Abstract

We examine stochastic reaction–diffusion equations of the form ∂u∂t=Au(t,x)+f(u(t,x))+σ(u(t,x))Ẇ(t,x) on a bounded spatial domain D⊂Rd, where f models a constrained, dissipative force that keeps solutions between −1 and 1. To model this, we assume that f(u),σ(u) are unbounded as u approaches ±1. We identify sufficient conditions on the growth rates of f and σ that guarantee solutions to not escape this bounded set.

Suggested Citation

  • Ivanhoe, John & Salins, Michael, 2025. "Preventing finite-time blowup in a constrained potential for reaction–diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:spapps:v:185:y:2025:i:c:s0304414925000687
    DOI: 10.1016/j.spa.2025.104627
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    References listed on IDEAS

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    1. Juan Yang & Jianliang Zhai & Qing Zhou, 2014. "The Small Time Asymptotics of SPDEs with Reflection," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, May.
    2. Juan Yang & Jianliang Zhai & Qing Zhou, 2014. "The Small Time Asymptotics of SPDEs with Reflection," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Doering, Charles R. & Mueller, Carl & Smereka, Peter, 2003. "Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 243-259.
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