Multi-scale analysis of SPDEs with degenerate additive noise

被引：19

作者：

Mohammed, Wael W. ^{[1
]}

Bloemker, Dirk ^{[2
]}

Klepel, Konrad ^{[2
]}

机构：

[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

[2] Univ Augsburg, Inst Math, D-86159 Augsburg, Germany

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2014年 / 14卷 / 02期

关键词：

Amplitude equation; multi-scale analysis; stabilization; stochastic partial differential equations; degenerate noise; EQUATION;

D O I：

10.1007/s00028-013-0213-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a quite general class of stochastic partial differential equations with quadratic and cubic nonlinearities and derive rigorously amplitude equations, using the natural separation of time-scales near a change of stability. We show that degenerate additive noise has the potential to stabilize or destabilize the dynamics of the dominant modes, due to additional deterministic terms arising in averaging. We focus on equations with quadratic and cubic nonlinearities and give applications to the Burgers' equation, the Ginzburg-Landau equation, and generalized Swift-Hohenberg equation.

引用

页码：273 / 298

页数：26