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This article is dedicated to insensitization issues of a quadratic functionalinvolving the solution of the linear heat equation with respect to domainsvariations. This work can be seen as a continuation of [P. Lissy, Y. Privat,and Y. Simpor\'e. Insensitizing control for linear and semi-linear heatequations with partially unknown domain. ESAIM Control Optim. Calc. Var.,25:Art. 50, 21, 2019], insofar as we generalize several of the results itcontains and investigate new related properties. In our framework, we considerboundary variations of the spatial domain on which the solution of the PDE isdefined at each time, and investigate three main issues: (i) approximateinsensitization, (ii) approximate insensitization combined with an exactinsensitization for a finite-dimensional subspace, and (iii) exactinsensitization. We provide positive answers to questions (i) and (ii) andpartial results to question (iii).

Insensitizing controls for the heat equation with respect to boundary variations