论文标题
关于边界变化的热方程式不敏感控制
Insensitizing controls for the heat equation with respect to boundary variations
论文作者
论文摘要
本文致力于二次功能的不敏化问题，涉及线性热方程相对于域变化的解决方案。这项工作可以看作是[P. Lissy，Y。Privat和Y.Simporé。对线性和半线性热方程的控制不敏感，具有部分未知域。 ESAIM控制最佳。计算。 var。，25：艺术。在我们概括其中包含的几个结果并研究新的相关属性的情况下，2019年第50、21、21、21、21、]。在我们的框架中，我们考虑了在每次定义PDE解决方案的空间结构域的边界变化，并研究了三个主要问题：（i）近似不敏感，（ii）近似不敏感的不敏感性与有限二维子空间和（III）精确的不敏化的确切不敏化。我们为问题（i）和（ii）和部分结果提供了积极的答案（iii）。
This article is dedicated to insensitization issues of a quadratic functional involving the solution of the linear heat equation with respect to domains variations. This work can be seen as a continuation of [P. Lissy, Y. Privat, and Y. Simporé. Insensitizing control for linear and semi-linear heat equations with partially unknown domain. ESAIM Control Optim. Calc. Var., 25:Art. 50, 21, 2019], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider boundary variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate insensitization, (ii) approximate insensitization combined with an exact insensitization for a finite-dimensional subspace, and (iii) exact insensitization. We provide positive answers to questions (i) and (ii) and partial results to question (iii).
