Abstract
A condition is identified that implies that solutions to the stochastic reaction-diffusion equation 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.
Citation
Michael Salins. "Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity." Electron. J. Probab. 27 1 - 17, 2022. https://doi.org/10.1214/22-EJP740
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