与域变化有关的热方程脱敏控制

S. Ervedoza, P. Lissy, Y. Privat
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引用次数: 2

摘要

.- 本文致力于研究涉及线性热方程求解的二次函数在域变化方面的脱敏问题。这项工作可以看作是 [28] 的延续,因为我们概括了其中的一些结果,并研究了新的相关性质。在我们的框架中,我们考虑了每次确定 PDE 解的空间域的变化,并研究了三个主要问题:(i) 近似脱敏,(ii) 近似脱敏与有限维子空间的精确脱敏相结合,以及 (iii) 精确脱敏。我们对问题(i)和(ii)给出了肯定的答案,对问题(iii)给出了部分结果。 pour
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Desensitizing control for the heat equation with respect to domain variations
. — This article is dedicated to desensitizing issues for a quadratic functional involving the solution of the linear heat equation with respect to domain variations. This work can be seen as a continuation of [28], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate desensitizing, (ii) approximate desensitizing combined with an exact desensitizing for a finite-dimensional subspace, and (iii) exact desensitizing. We provide positive answers to questions (i) and (ii) and partial results to question (iii). pour
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