论半线性演化方程的精确全局可控性

Pub Date : 2024-07-08 DOI:10.1134/s0012266124030091

A. V. Chernov

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引用次数: 0

摘要

摘要对于与希尔伯特空间中带有算子（不一定是有界的）的受控半线性演化方程相关的考奇问题，我们获得了在任意固定（无附加约束）时间间隔上精确可控性进入给定终态（以及在中间时刻进入给定中间状态）的充分条件。在这里，我们使用了布劳德-明蒂定理（Browder-Minty theorem），以及受控系统解连续延续到中间状态的链式技术。作为示例，我们考虑了一个半线性假抛物方程和一个半线性波方程。

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On the Exact Global Controllability of a Semilinear Evolution Equation

Abstract

For the Cauchy problem associated with a controlled semilinear evolution equation with an operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact controllability into a given terminal state (and also into given intermediate states at interim time moments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the Browder—Minty theorem and also a chain technology of successive continuation of the solution of the controlled system to intermediate states. As examples, we consider a semilinear pseudoparabolic equation and a semilinear wave equation.

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