<p style='text-indent:20px;'>In this article we develop the theory of stable invariant manifolds for evolution equations with application to control problem. We will construct invariant subspaces for linear equations which can be extended to the non-linear equations in the neighbourhood of the equilibrium with help of perturbation theory. Here will be considered both cases of the discrete and continuous spectrum of the generator associated with resolving semi-group. The example of global invariant manifold will be presented for Burgers equation.</p>

中文翻译：

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用于控制问题的稳定不变流形

<p style='text-indent:20px;'>在本文中，我们开发了用于控制问题的演化方程的稳定不变流形理论。我们将构造线性方程的不变子空间，借助微扰理论，可以将其扩展到平衡附近的非线性方程。这里将考虑与分解半群相关的生成器的离散和连续谱的两种情况。Burgers方程以全局不变流形为例。</p>