Abstract

In this talk, we are concerned with minimal control time for linear hyperbolic systems of balance laws.  We will show how such critical quantities depend on internal and boundary couplings under various types of controllability (exact controllability (EC), null-controllability (NC), boundary controllability (BC) and internal controllability (IC)).  A key aspect will be demonstrated that the minimal time can be strictly smaller than the classical one proposed by J.-M. Coron, T.T. Li and D. Russell etc. In particular, for EC, we will show that the minimal time is invariant with respect to the internal couplings, while for NC,  a recursive algorithm will be proposed to characterize this critical quantity. This talk is based on joint works with Guillaume Olive.