Geodesic
To substantiate correctness of optimal control problem of wave equation with controllable differentiation operator
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 61-68
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We consider ways to construct generalized solutions of wave equation with discontinuous coefficient with respect to spacial variable of differentiation operator.
Keywords: wave equation, hyperbolic systems, method of characteristics, method of successive approximations. 
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V. A. Terletsky; O. V. Bochkova. To substantiate correctness of optimal control problem of wave equation with controllable differentiation operator. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 61-68. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a5/

[1] V. A. Terletskii, E. A. Lutkovskaya, “Variatsionnyi printsip maksimuma v zadache optimalnogo upravleniya nelineinymi volnovymi protsessami”, Izv. Irkut. gos. un-ta. Ser. Matematika, 3:3 (2010), 105–117 | MR | Zbl

[2] V. A. Terletskii, E. A. Lutkovskaya, “Obobschennoe reshenie nelineinogo volnovogo uravneniya s nelineinymi granichnymi usloviyami pervogo, vtorogo i tretego roda”, Differents. uravneniya, 45:3 (2009), 403–415 | MR | Zbl