Geodesic
Statement of border tasks on the plane dependent on the coefficients for the type of the wave equation. III
Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 44-52 
V. I. Korzyuk; I. S. Kozlovskaja; S. N. Naumavets. Statement of border tasks on the plane dependent on the coefficients for the type of the wave equation. III. Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 44-52. http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is a continuation of [1, 2] under the general title. In the half-strip on the plane of two independent variables, boundary value problems for a second-order hyperbolic equation with constant coefficients are considered, whose operator represents a composition of first-order operators. The simplest problems are considered where Cauchy and Dirichlet conditions are attached at the boundary of the domain. We consider the correct problems, the solutions of which in an analytical form are presented.

[1] Korzyuk V. I., Kozlovskaya I. S., Naumovets S. N., “Postanovka granichnykh zadach na ploskosti v zavisimosti ot koeffitsientov dlya tipa volnovogo uravneniya. I”, Trudy Instituta matematiki, 27:1 (2019), 29–36

[2] Korzyuk V. I., Kozlovskaya I. S., Naumovets S. N., “Postanovka granichnykh zadach na ploskosti v zavisimosti ot koeffitsientov dlya tipa volnovogo uravneniya. II”, Trudy Instituta matematiki, 27:1 (2019), 37–43

[3] Korzyuk V. I., Kozlovskaya I. S., Klassicheskie resheniya zadach dlya giperbolicheskikh uravnenii, V desyati chastyakh, v. 1, Minsk, 2017, 45 pp.

[4] Korzyuk V. I., Kozlovskaya I. S., Klassicheskie resheniya zadach dlya giperbolicheskikh uravnenii, V desyati chastyakh, v. 2, Minsk, 2017, 52 pp.

[5] Korzyuk V. I., Naumovets S. N., Sevostyuk V. A., “O klassicheskom reshenii vtoroi smeshannoi zadachi dlya odnomernogo volnovogo uravneniya.”, Trudy Instituta matematiki, 26:1 (2018), 35–42

[6] Korzyuk V. I., Naumovets S. N., Serikov V. P., “Metod kharakteristicheskogo parallelogramma resheniya vtoroi smeshannoi zadachi dlya odnomernogo volnovogo uravneniya.”, Trudy Instituta matematiki, 26:1 (2018), 43–53

[7] Korzyuk V. I., Naumovets S. N., “Klassicheskoe reshenie smeshannoi zadachi dlya odnomernogo volnovogo uravneniya s proizvodnymi vysokogo poryadka v granichnykh usloviyakh”, Dokl. NAN Belarusi, 60:3 (2016), 11–17

[8] Moiseev E. I., Korzyuk V. I., Kozlovskaya I. S., “Klassicheskoe reshenie zadachi s integralnym usloviem dlya odnomernogo volnovogo uravneniya”, Differentsialnye uravneniya, 50:10 (2014), 1373–1385

[9] Korzyuk V. I., Kozlovskaya I. S., Naumovets S. N., “Klassicheskoe reshenie pervoi smeshannoi zadachi odnomernogo volnovogo uravneniya s usloviyami tipa Koshi”, Ves. Nats. akad. navuk Belarusi. Ser. fiz.-mat. navuk, 2015, no. 1, 7–20