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arXiv · 2107.04459

Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity

Michael Salins
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Abstract

A condition is identified that implies that solutions to the stochastic reaction-diffusion equation $\frac{\partial u}{\partial t} = \mathcal{A} u + f(u) + σ(u) \dot{W}$ 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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Michael Salins. 2021-12-09. Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity. https://arxiv.org/abs/2107.04459

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