Séminaires : Dynamical systems and PDEs

Equipe(s) : gd,
Responsables :Sergei Kuksin, Dmitrii Treschev
Email des responsables : sergei.kuksin@imj-prg.fr
Salle : https://mi-ras-ru.zoom.us/j/98541889798?pwd=SGdnT2lPWCtrbzNjOHQyb09NS0dXdz09
Adresse :Zoom
Description Paris 7 Diderot & Steklov Mathematical Institute Online Seminar

Orateur(s) Armen Shirikyan - University of Cergy-Pontoise,
Titre Global stabilisation of damped-driven conservation laws by a one-dimensional forcing
Horaire16:00 à 17:00
RésumeWe 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 stabilized 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 localized control. The proofs are based on the strong dissipation property of the PDEs in question and the theory of positivity preserving semigroups.