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

John Ivanhoe; Michael Salins

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

Probability 2024-06-26 v2

Authors: John Ivanhoe , Michael Salins

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.

Keywords

nonlinear diffusion equations blow-up for partial differential equations reaction-diffusion systems

Cite

@article{arxiv.2406.15672,
  title  = {Preventing Finite-Time Blowup in a Constrained Potential for Reaction-Diffusion Equations},
  author = {John Ivanhoe and Michael Salins},
  journal= {arXiv preprint arXiv:2406.15672},
  year   = {2024}
}

Comments

18 pages

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