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@article{faucris.324796795,
abstract = {The optimal control problems for the wave equation are considered on networks. The
turnpike property is shown for the state equation, the adjoint state equation as well as
the optimal cost. The shape and topology optimization is performed for the network
with the shape functional given by the optimality system of the control problem.
The set of admissible shapes for the network is compact in finite dimensions, thus
the use of turnpike property is straightforward. The topology optimization is analysed
for an example of nucleation of a small cycle at the internal node of network. The
topological derivative of the cost is introduced and evaluated in the framework of
domain decomposition technique. Numerical examples are provided.