Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity
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Date
2022-01-01
Authors
Salins, Michael
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Citation
M. Salins. 2022. "Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity." Electronic Journal of Probability, Volume 27, article no. 12, pp. 1–17. https://doi.org/10.1214/22-ejp740
Abstract
A condition is identified that implies that solutions to the stochastic reaction-diffusion
equation ∂u
∂t = Au + f(u) + σ(u)W˙ on a bounded spatial domain never explode.
We consider the case where σ grows polynomially and f is polynomially dissipative,
meaning that f strongly forces solutions toward finite values. This result demonstrates
the role that the deterministic forcing term f plays in preventing explosion
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Copyright 2022 the Author(s). This work is distributed under a Creative Commons Attribution 4.0 License. (https://creativecommons.org/licenses/by/4.0/)