Global boundary controllability of the de St. Venant equations between steady states

By Martin Gugat, Günter Leugering. 2003

113 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/130afd921716fce89f4d258d942e9f858c9ace1d

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In Control and Systems Engineering

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

On the controllability of the 1-D isentropic Euler equation (2007, background): “Let us remark also that for (EI) the particular case γ = 2 corresponds to the Saint-Venant (or shallow-water) equation, for which several controllability problems have been considered in the framework of C1 solutions (see for instance [16, 23]).”
Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs (2018, unknown): “It is easily seen that βtt(1, t) = vtt(1, t) + pψ(1, 1)ut(1, t) − pψ(1, 0)ut(0, t) + p ( pψy(1, 1) + c2φ(1, 1) ) u(1, t) − p ( pψy(1, 0) + c2φ(1, 0) ) u(0, t) − pφ(1, 1)vt(1, t) + (pφ(1, 0) − γ(1)B) vt(0, t) − γ(1)A2X(t) − p ( c1ψ(1, 1) − pφy(1, 1) ) v(1, t) + ( pc1ψ(1, 0) − p(2)φy(1, 0) − γ(1)AB ) ”
Global controllability between steady supercritical flows in channel networks (2004, background): “In the engineering literature, the term F(h;U ) from (4) is often called the friction slope (see Reference [10, p. 13]).”
High detail stationary optimization models for gas networks (2014, background): “…in theoretical studies of controllability and stabilization of gas flow (Banda and Herty 2008; Banda et al. 2006; Brouwer et al. 2006; Gugat 2003; Gugat and Leugering 2003; Gugat et al. 2007; Leugering and Schmidt 2002), which are currently restricted to very small networks without discrete…”
Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping (2011, background): “The quasilinear case is of interest since many relevant physical systems are described by 2 × 2 systems of first-order hyperbolic quasilinear PDEs, such as open channels [11, 16, 17, 18], transmission lines [6], gas flow pipelines [14] or road traffic models [12].”
Domain Decomposition Methods in Optimal Control of Partial Differential Equations (2004, background): “[13], Gugat and Leugering [33], Gugat, Leugering and Schmidt [34] and Gugat [31].”