Null controllability of a cascade system of parabolic-hyperbolic equations
The paper treats the null controllability of a cascade linear system formed by a heat and a wave equation in a cylinder \(\Omega \times (0,T)\), where \(\Omega \in \mathbb R^N\) is a bounded domain of class \(C^2\). The control acts only on the heat equation and is supported by a set of the form \(\omega \times (0,T)\), \(\omega\) being a nonempty, open subset of \(\Omega\). In the wave equation, only the restriction of the solution to the heat equation to another set \({\mathcal O} \times (0,T)\) appears. It is proved that under appropriate assumptions concerning \(T, \omega\) and \({\mathcal O}\), the system is null controllable.
coupled systems of partial differential equations
scientific article; zbMATH DE number 2110783