Scholarlink

<p>An abstract nonautonomous parabolic linear-quadratic regulator problem with very general final cost operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P_{T}\)</EquationSource> </InlineEquation> is considered, subject to the same assumptions under which a classical solution of the associated differential Riccati equation was shown to exist, in two papers appeared in 1999 and 2000, by Terreni and the first named author. We prove an optimal uniqueness result for the integral Riccati equation in a wide and natural class, filling a gap existing in the autonomous case, too. In addition, we give a regularity result for the optimal state.</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

An Optimal Uniqueness Result for Riccati Equations Arising in Abstract Parabolic Control Problems

  • 期刊论文

  • 发表日期：

    2026年1月9日

查看全文
  • Paolo Acquistapace,
  • Francesco Bartaloni

摘要

An abstract nonautonomous parabolic linear-quadratic regulator problem with very general final cost operator \(P_{T}\) is considered, subject to the same assumptions under which a classical solution of the associated differential Riccati equation was shown to exist, in two papers appeared in 1999 and 2000, by Terreni and the first named author. We prove an optimal uniqueness result for the integral Riccati equation in a wide and natural class, filling a gap existing in the autonomous case, too. In addition, we give a regularity result for the optimal state.