Sentinels for periodic distributed systems (Q919533)

The periodic distributed systems \[ \partial y/\partial t-\Delta y+f(y)=0\text{ in } \Omega \times (0,T), \] where \(\Omega\) is an open set of \({\mathbb{R}}^ n\), bounded or not, with a smooth boundary \(\Gamma\), \(\Delta y=\partial^ 2y/\partial x^ 2_ 1+...+\partial^ 2y/\partial x^ 2_ n\), solutions periodic in time \(y(x,0)=y(x,T)\) are to find with boundary conditions \(y=\bar y+\tau \hat y\) on \(\Gamma\times (0,T)\) where \(\bar y\) is known and \(\tau\) \(\bar y\) denotes the ``perturbation''. The author reduces the ``sentinels'' problem to a problem of controllability and uses suitable adaptions of Hilbert uniqueness method to give solutions to the original problem.