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Start Over Descriptor "Itô’s formula" Topic existence theorems Topic stochastic analysis Journal journal of differential equations
1 results on '"Itô’s formula"'

1. Impacts of noise on a class of partial differential equations.

Author

Lv, Guangying and Duan, Jinqiao

Subjects
*PARTIAL differential equations, *SET theory, *EXISTENCE theorems, *MATHEMATICAL singularities, *STOCHASTIC analysis
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 partial differential 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. [ABSTRACT FROM AUTHOR]

Published
2015
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