14:00h – 14:40h

Equivalent 1D first-order linear hyperbolic systems and null controllability

In this talk, we present some recent and new results about the minimal null control time for first-order linear hyperbolic systems in dimension one. More precisely, we completely characterize the smallest and largest values that this time can take with respect to the internal coupling matrix. We give explicit and easy-to-compute formulas. The proof relies on several methods: the backstepping method, a canonical LU decomposition for boundary coupling matrices and a compactness-uniqueness method adapted to the null controllability property. This is based on a joint work with Long Hu.

14:50h – 15:30h

Optimal control problems for a class of chemotaxis models

Chemotaxis models attempt to reproduce the biological process in which the spatial transport of the density of a living organism is modified by the presence of a chemical substance. The production and/or consumption of chemical substances by cells, the degradation of chemical reactions or logistics for living organisms are other interactions that can also be taken into account in mathematical modelling.
Introducing a control over the system can be suitable for several purposes. The optimal control problem and obtaining first-order optimality conditions for local optimal solutions are also some interesting topics to be discussed in this talk.