Geodesic
Classical solution of the boundary-value problem for hyperbolic equation in half-region
Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 64-74.

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Using method of characteristics the analytical solution of the first problem for the hyperbolic equation $(\partial_t-a^{(1)}\partial_x+b^{(1)})(\partial_t-a^{(2)}\partial_x+b^{(2)})u=f(t,x),$ is under construction. Conditions of the coordination of initial and boundary condition are deduced. 
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V. I. Korzyuk; E. S. Cheb; A. A. Karpechina. Classical solution of the boundary-value problem for hyperbolic equation in half-region. Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 64-74. http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a6/

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