Null controllability using flatness: A case study of a 1-D heat equation with discontinuous coefficients

The approach recently proposed by the authors for the null controllability of 1-D parabolic equations is applied to the nontrivial case of a heat equation with discontinuous coefficients and subjected to Robin boundary conditions. The control steering the system to zero from a discontinuous initial state is comprehensively derived, together with the corresponding trajectory. Numerical experiments illustrate several features of the theory and demonstrate its effectiveness.