Geodesic
Solution of the wave equation in a quarter plane
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 40-56.

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In this article, the classical solution in the class of continuously differentiable functions of arbitrary order in the quarter plane for the wave equation is presented in an analytical form. The classical solution of the equation under consideration is determined. To construct this solution, a partial solution of the original wave equation is written out. For the given functions, the obtained matching conditions are necessary and sufficient for the presented solution of the equation to be classical of high order of smoothness. 
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V. I. Korzyuk; I. S. Kozlovskaja; V. Yu. Sokolovich. Solution of the wave equation in a quarter plane. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 40-56. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a4/

[1] Korzyuk V. I., Kozlovskaya I. S., Sokolovich V. Yu., “Klassicheskoe reshenie v chetverti ploskosti smeshannoi zadachi dlya volnovogo uravneniya so smeshannymi usloviyami”, Doklady NAN Belarusi, 62:6 (2018), 647–651 | MR

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

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

[4] 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 | MR | Zbl

[5] Korzyuk V. I., Kozlovskaya I. S., “Reshenie zadachi Koshi giperbolicheskogo uravneniya dlya odnorodnogo differentsialnogo operatora v sluchae dvukh nezavisimykh peremennykh”, Doklady NAN Belarusi, 55:5 (2011), 9–13 | MR | Zbl

[6] Korzyuk V. I., Kozlovskaya I. S., Kozlov A. I., “Caushy problem in half-plan for hyperbolic equation on a half-plane with constant coefficients”, Analytic methods of analysis and differential equations, AMA Cambridge scientific publishers, 2014, 45–71 | MR | Zbl

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

[8] Korzyuk V. I., Kozlovskaya I. S., “Ob usloviyakh soglasovaniya v granichnykh zadachakh dlya giperbolicheskikh uravnenii”, Doklady NAN Belarusi, 57:5 (2013), 37–42 | MR | Zbl

[9] Korzyuk V. I., Cheb E. S., Karpechina A. A., “Klassicheskoe reshenie pervoi smeshannoi zadachi v polupolose dlya lineinogo giperbolicheskogo uravneniya vtorogo poryadka”, Trudy Instituta matematiki, 20:2 (2012), 64–74 | MR | Zbl