| Abstract: |
| In this talk, we are interested in an insensitizing control problem on a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, which consists in finding a distributed control such that some functional of the state is insensitive at the first order to the perturbations of the domain. Our first result consists of an approximate insensitization property on the semi-linear heat equation. It rests upon a linearization procedure together with the use of an appropriate fixed point theorem. Our second result is specific to the linear case. We show a property of exact insensitization for some families of deformation given by one or two parameters. Our proof relies on a geometrical approach and direct computations. |
|