Global Synchronising Behavior of Evolution Equations with Exponentially Growing Nonautonomous Forcing
Global Synchronising Behavior of Evolution Equations with Exponentially Growing Nonautonomous Forcing
复制标题
具有指数增长非自主强迫的演化方程的全局同步行为
DOI：
10.3934/cpaa.2018091
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Desheng Li
中科院分区：
文献类型：
--
作者：
Xuewei Ju;Desheng Li
本文研究Banach空间X上的非自治发展系统.x(T)+Ax=f(x，h(T))，(0.1).其中A是X上的双曲扇形算子，非线性度f是C(X-αx X，X)中的一个元素，非自治强迫h是C(R，X)中的一个元素.在一些合理的假设下，我们首先在余循环半流的框架下建立了系统唯一的非自治双曲平衡点的存在性结果。然后，我们证明了随着时间的变化，系统表现出与非自治强迫h的全局同步行为。最后，我们将抽象结果应用于具有加性白噪声的随机偏微分方程解，得到了相应系统的随机双曲平衡点。
This work is concerned with the following nonautonomous evolutionary system on a Banach space X, .x(t) + Ax = f (x, h(t)), ( 0.1) .where A is a hyperbolic sectorial operator on X, the nonlinearity f is an element of C (X-alpha x X, X) is Lipschitz in the first variable, the nonautonomous forcing h is an element of C (R, X) is mu-subexponentially growing for some mu > 0 (see (3.4) below for definition). Under some reasonable assumptions, we first establish an existence result for a unique nonautonomous hyperbolic equilibrium for the system in the framework of cocycle semiflows. We then demonstrate that the system exhibits a global synchronising behavior with the nonautonomous forcing h as time varies. Finally, we apply the abstract results to stochastic partial differential equations with additive white noise and obtain stochastic hyperbolic equilibria for the corresponding systems.