Special Session 2: PDEs and Applications

Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation

Peipei Shang
Tongji University
Peoples Rep of China
Co-Author(s):    Georges Bastin, Jean-Michel Coron, Amaury Hayat
Abstract:
We study the exponential stabilization of a shock steady state for the inviscid Burgers equation on a bounded interval. Our analysis relies on the construction of an explicit strict control Lyapunov function. We prove that by appropriately choosing the feedback boundary conditions, we can stabilize the state as well as the shock location to the desired steady state in $H^2$-norm, with an arbitrary decay rate.