Scholarlink

Abstract <p> For the Cauchy problem associated with a controlled semilinear evolution equation withbounded time-varying operator in a Hilbert space, we obtain sufficient conditions for the exactcontrollability to a given final state (and also to given intermediate states at intermediate timeinstants) on an arbitrarily (without additional conditions) fixed time interval. In fact, wegeneralize a similar result formerly obtained by the author for the case of a constant operator;here we use the Minty–Browder theorem and also the chaining technique of successivecontinuation of the solution of a control system to intermediate states. By way of example (whichis of specific interest) we consider a semilinear equation describing the global electric circuit in theEarth atmosphere.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On Exact Global Controllability of a Semilinear Evolution Equation with a Time-Varying Operator

  • 期刊论文

  • 发表日期：

    2025年3月1日

查看全文
  • A. V. Chernov

摘要

Abstract

For the Cauchy problem associated with a controlled semilinear evolution equation withbounded time-varying operator in a Hilbert space, we obtain sufficient conditions for the exactcontrollability to a given final state (and also to given intermediate states at intermediate timeinstants) on an arbitrarily (without additional conditions) fixed time interval. In fact, wegeneralize a similar result formerly obtained by the author for the case of a constant operator;here we use the Minty–Browder theorem and also the chaining technique of successivecontinuation of the solution of a control system to intermediate states. By way of example (whichis of specific interest) we consider a semilinear equation describing the global electric circuit in theEarth atmosphere.