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Wang, Ke; Gu, Qilong

Exact boundary controllability of nodal profile for quasilinear wave equations in a planar tree-like network of strings. (English) Zbl 1295.35333

Math. Methods Appl. Sci. 37, No. 8, 1206-1218 (2014).
The paper deals with a quasilinear 1D wave equation. Classical piecewise \(C^2\) solutions are considered. The authors extend known result on local exact boundary controllability of nodal profile for 1D quasilinear wave equation in a single string to the case of a planar tree-like network of strings with general topology. A star-like network of strings is considered and the exact boundary controllability of nodal profile on a simple (or multiple) node is established. Then, the results are generalized to a tree-like network. The authors present the principles of providing nodal profiles, choosing and transfering boundary controls, and get the relationship between the number of given nodal profiles and the number of required boundary controls.
Reviewer: Vyacheslav I. Maksimov (Ekaterinburg)

Cited in 7 Documents

MSC:

35L72 Second-order quasilinear hyperbolic equations
93B05 Controllability
35L20 Initial-boundary value problems for second-order hyperbolic equations

Keywords:

quasilinear wave equations; exact boundary controllability of nodal profile; planar tree-like network of strings; star-line network; tree-like network; number of required boundary controls
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References:

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