扩散方程在可测集上的能观性估计和时间最优控制bang-bang性
Observability from measurable sets for diffusion equations and the bang–bang property of time optimal controls
摘要点击 506  全文点击 120  投稿时间:2021-04-26  修订日期:2022-02-24
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DOI编号  10.7641/CTA.2021.10352
  2022,39(9):1594-1600
中文关键词  能观性不等式, 零能控性, 可测集, 时间最优控制
英文关键词  observability  controllability  measurable sets  time optimal control
基金项目  国家自然科学基金项目(11971363), 武汉大学青年学术团队建设项目(413100085)资助.
作者单位E-mail
张灿 武汉大学 数学与统计学院 canzhang@whu.edu.cn 
中文摘要
      在前期工作[4–7]中, 笔者证明当观测集是Lebesgue正可测集时, 具有实解析系数抛物方程的能观性不等式成立. 在这些工作中, 笔者主要用到此类偏微分方程的解在正可测集上的定量估计式. 在这篇文章中, 将运用文献[19]的结论, 建立有界区域上具有非实解析系数扩散方程在时空区域Lebesgue可测集上的能观性不等式. 作为应用,本文将给出相应的时间或范数最优控制问题的bang–bang性.
英文摘要
      In our earlier works[4–7], we have proved observability inequalities from measurable sets hold for solutions of parabolic-type partial differential equations with real analytic coefficients in bounded domains. In these works, we have mainly utilized the propagation estimate of smallness for real analytic functions, and a telescoping series method. In the present paper, we shall establish the observability and controllability on measurable subsets in space and time variables for diffusion equations in bounded domains, without real analyticity assumptions on diffusion coefficients. As applications, we shall show bang–bang properties of time and norm optimal control problems governed by diffusion equations.