Special Session 158: From PDE control to the qualitative study of (random) dynamical systems
Feedback stabilization of entropy solutions to the p-system at a junction
Nicola De Nitti
University of Pisa Italy
Co-Author(s): G. M. Coclite, N. De Nitti, M. Garavello, F. Marcellini
Abstract:
We consider the p-system in Eulerian coordinates on a star-shaped network. Under suitable transmission conditions at the junction and dissipative boundary conditions in the exterior vertices, we show that the entropy solutions of the system are exponentially stabilizable. Our proof extends the strategy by Coron et al. (2017) and is based on a front-tracking algorithm used to construct approximate piecewise constant solutions whose BV norms are controlled through a suitable exponentially-weighted Glimm-type Lyapunov functional.