Exact boundary controllability of nodal profile for Saint-Venant system on a network with loops. (English. French summary) Zbl 1423.35245
Summary: The exact boundary controllability for hyperbolic systems can not be realized generally on a network with loops (see [the third author et al., Discrete Contin. Dyn. Syst. 28, No. 1, 243–257 (2010; Zbl 1211.93024)]). In this paper we consider the exact boundary controllability of nodal profile on a network with loops. Precisely speaking, on a network with a triangle-like loop, when nodal profiles are given at various kinds of nodes, different constructive methods can be used to get the corresponding exact boundary controllability of nodal profile for Saint-Venant system by means of boundary controls acting on suitable nodes, respectively. This reveals that the exact boundary controllability of nodal profile is quite different from the usual exact boundary controllability, and has relatively distinctive behaviors and characters.
MSC:
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35L65 | Hyperbolic conservation laws |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35L02 | First-order hyperbolic equations |
Citations:
Zbl 1211.93024References:
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