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

John Ivanhoe and Michael Salins

Stochastic Processes and their Applications, 2025, vol. 185, issue C

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.

Keywords: Stochastic heat equation; Stochastic reaction–diffusion equation; Constrained potential; Explosion; Blow-up; Global solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104627

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