Hirsch-Dick M, Gugat M, Leugering G (2011)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2011
Publisher: American Institute of Mathematical Sciences (AIMS)
Book Volume: 1
Pages Range: 225-244
Journal Issue: 2
URI: http://www.aimsciences.org/journals/displayReferences.jsp?paperID=6330
We study the isothermal Euler equations with friction and consider non-stationary solutions locally around a stationary subcritical state on a finite time interval. The considered control system is a quasilinear hyperbolic system with a source term. For the corresponding initial-boundary value problem we prove the existence of a continuously differentiable solution and present a method of boundary feedback stabilization. We introduce a Lyapunov function which is a weighted and squared H1-norm of the difference between the nonstationary and the stationary state. We develop boundary feedback conditions which guarantee that the Lyapunov function and the H1-norm of the difference between the non-stationary and the stationary state decay exponentially with time. This allows us also to prove exponential estimates for the C0- and C1- norm.
APA:
Hirsch-Dick, M., Gugat, M., & Leugering, G. (2011). A strict H1-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Numerical Algebra, Control and Optimization, 1(2), 225-244. https://dx.doi.org/10.3934/naco.2011.1.225
MLA:
Hirsch-Dick, Markus, Martin Gugat, and Günter Leugering. "A strict H1-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction." Numerical Algebra, Control and Optimization 1.2 (2011): 225-244.
BibTeX: Download