Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case
Averaging principle for non autonomous slow-fast systems of stochastic RDEs: the almost periodic case
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发表时间：
2016-02
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通讯作者：
S. Cerrai;A. Lunardi
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作者：
S. Cerrai;A. Lunardi
研究了一类慢-快随机反应扩散方程组的平均原理的有效性。我们假设这里的系数的快速方程依赖于时间，使经典配方的平均原则的不变措施的快速方程不再可用。作为一种替代方案，我们引入了与快速方程相关的随时间演化的措施。在快方程中的系数是概周期的假设下，测度族的演化是概周期的。这允许识别适当的平均方程并证明平均极限的有效性。
We study the validity of an averaging principle for a slow-fast system of stochastic reaction diffusion equations. We assume here that the coefficients of the fast equation depend on time, so that the classical formulation of the averaging principle in terms of the invariant measure of the fast equation is not anymore available. As an alternative, we introduce the time depending evolution family of measures associated with the fast equation. Under the assumption that the coefficients in the fast equation are almost periodic, the evolution family of measures is almost periodic. This allows to identify the appropriate averaged equation and prove the validity of the averaging limit.