|
SEMINARS |
Dynamical Systems and PDEs
|
|||
|
Global stabilisation of damped-driven conservation laws by a one-dimensional forcing A. R. Shirikyan University of Cergy-Pontoise |
|||
Abstract: We study a multidimensional conservation law in a bounded domain, subject to a damping and an external force. Imposing the Dirichlet boundary condition and using standard methods of parabolic PDEs, it is straightforward to check that all the solutions are bounded in a Hölder space. Our main result proves that any trajectory can be exponentially stabilised by a one-dimensional external force supported in a given open subset. As a consequence, we obtain the global approximate controllability to trajectories by a one-dimensional localised control. The proofs are based on the strong dissipation property of the PDEs in question and the theory of positivity preserving semigroups. Language: English Website: https://zoom.us/j/91585712972?pwd=Skh0S09ML2lFMUg2YlVBcjBMQ0dBdz09 |