Multi-scale analysis of SPDEs with degenerate additive noise
Multi-scale analysis of SPDEs with degenerate additive noise
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DOI：
10.1007/s00028-013-0213-3
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发表时间：
2014-06-01
影响因子：
1.4
通讯作者：
Klepel, Konrad
中科院分区：
文献类型：
--
作者：
Mohammed, Wael W.;Bloemker, Dirk;Klepel, Konrad
我们考虑一类相当一般的具有二次和三次非线性的随机偏微分方程组，利用时间尺度在稳定性变化附近的自然分离，严格地推导出振幅方程。我们证明了简并的加性噪声有可能稳定或破坏主模的动力学，这是由于在平均过程中产生了额外的确定项。我们主要讨论具有二次和三次非线性的方程，并给出了它们在Burgers方程、Ginzburg-Landau方程和广义Swift-Hohenberg方程中的应用。
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.