Controls insensitizing the norm of the solution of a semilinear heat equation (Q1910030)

The authors consider a semilinear heat equation with partially known initial and boundary conditions. It is shown that the so-called insensitivity conditions are equivalent to a particular nonlinear exact controllability problem for parabolic equations. Solving the linear problem leads to the proof of a non-trivial uniqueness property which is also used to characterize a particular subset of the admissible controls. This characterization is made thanks to a convex duality theorem and allows the authors to use a fixed-point theorem and get the result for the nonlinear case.