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 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[2] Korzyuk V. I., Cheb E. S., Shirma M. S., “Reshenie pervoi smeshannoi zadachi dlya volnovogo uravneniya metodom kharakteristik”, Trudy In-ta matematiki NAN Belarusi, 17:2 (2009), 23–34

[3] Korzyuk V. I., Cheb E. S., Le Tkhi Tkhu, “Reshenie smeshannoi zadachi dlya bivolnovogo uravneniya metodom kharakteristik”, Trudy In-ta matematiki NAN Belarusi, 18:2 (2010), 36–54 | MR | Zbl

[4] Korzyuk V. I., Cheb E. S., Le Tkhi Tkhu, “Reshenie pervoi smeshannoi zadachi dlya nestrogo bivolnovogo uravneniya”, Doklady NAN Belarusi, 55:4 (2011), 5–13 | MR

[5] Korzyuk V. I., “Metod energeticheskikh neravenstv i operatorov osredneniya”, Vestnik BGU. Ser. 1, 1996, no. 3, 55–71 | MR | Zbl

[6] Korzyuk V. I., Kozlovskaya I. S., “Reshenie zadachi Koshi dlya giperbolicheskogo uravneniya s postoyannymi koeffitsientami v sluchae dvukh nezavisimykh peremennykh”, Differents. uravneniya, 48:5 (2012), 700–709 | Zbl

[7] Korzyuk V. I., Uravneniya matematicheskoi fiziki, M., 2011