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arXiv · 1402.6365

Impacts of Noise on a Class of Partial Differential Equations

Guangying Lv·Jinqiao Duan
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Abstract

This paper is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic parabolic equations. Then, we prove that noise could induce singularities (finite time blow up of solutions). Finally, we show that a stochastic Allen-Cahn equation does not have finite time singularities and the unique solution exists globally.

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Guangying Lv, Jinqiao Duan. 2014-02-25. Impacts of Noise on a Class of Partial Differential Equations. https://arxiv.org/abs/1402.6365

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