Impacts of Noise on a Class of Partial Differential Equations
Analysis of PDEs
2014-10-14 v2
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.
Keywords
Cite
@article{arxiv.1402.6365,
title = {Impacts of Noise on a Class of Partial Differential Equations},
author = {Guangying Lv and Jinqiao Duan},
journal= {arXiv preprint arXiv:1402.6365},
year = {2014}
}
Comments
20 pages