250 2019 eng 264 289 1 57 article 0 2019-02-01 2019-02-06 -- We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval (0,T) that depends on the boundary traces of the solution. If the time horizon T is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for T to infinity the approximation error converges to zero in the sense of the norm in L^2(0,1) with the rate 1/T, if the time interval (0,T) is transformed to the fixed interval (0,1). Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If T is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations. SIAM Journal on Control and Optimization 10.1137/17M1134470 epub ahead of print 2 Creative Commons - CC BY - Namensnennung 4.0 International Martin Gugat Falk Hante Friedrich-Alexander-Universität Erlangen-Nürnberg A03 C03 https://opus4.kobv.de/opus4-trr154/files/250/siamturnpikefinalREVISION2.pdf