Gugat M, Hirsch-Dick M (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: 469-491
Journal Issue: 4
URI: http://aimsciences.org/journals/contentsListnew.jsp?pubID=483
We consider the isothermal Euler equations with friction that model the gas flow through pipes. We present a method of time-delayed boundary feedback stabilization to stabilize the isothermal Euler equations locally around a given stationary subcritical state on a finite time interval. The considered control system is a quasilinear hyperbolic system with a source term. For this system we introduce a Lyapunov function with delay terms and develop time-delayed boundary controls for which the Lyapunov function decays exponentially with time. We present the stabilization method for a single gas pipe and for a star-shaped network of pipes.
APA:
Gugat, M., & Hirsch-Dick, M. (2011). Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Mathematical Control and Related Fields, 1(4), 469-491. https://dx.doi.org/10.3934/mcrf.2011.1.469
MLA:
Gugat, Martin, and Markus Hirsch-Dick. "Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction." Mathematical Control and Related Fields 1.4 (2011): 469-491.
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