Geodesic
Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 605-624

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For the wave equation, time-optimal control problems with two-sided boundary controls of three basic types are considered in classes of weak generalized solutions. Stable algorithms for computing approximate optimal times and optimal boundary controls are developed by modifying algorithms proposed earlier for the case of strong generalized solutions. The approximate solutions are proved to converge as the parameters of the finite-dimensional approximation are asymptotically refined and the errors in the specified terminal functions are reduced. 
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     title = {Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a2/}
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D. A. Ivanov; M. M. Potapov. Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 605-624. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a2/