Classical solution of the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions
https://doi.org/10.29235/1561-24302019-55-4-406-412
Abstract
This paper considers the mixed problem for a one-dimensional wave equation with second-order derivatives at boundary conditions. Using the method of characteristics, a classical solution to this problem is found in analytical form. Its uniqueness is proved under the relevant compatibility conditions.
About the Authors
V. I. Korzyuk
Institute of Mathematics of the National Academy of Sciences of Belarus; Belarusian State University
Belarus
Belarus
Viktor I. Korzyuk – Academician, Professor, Dr. Sc. (Physics and Mathematics).
11, Surganov Str., 220072, Minsk; 4, Nezavisimosti Ave., 220030, Minsk
S. N. Naumavets
Brest State Technical University
Belarus
Belarus
Sviatlana N. Naumavets – Senior Lecturer.
267, Moskovskaya Str., 224017, Brest
V. A. Sevastyuk
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Vladimir A. Sevastyuk – Engineer.
11, Surganov Str., 220072, Minsk.
References
1. Korzyuk V. I., Kozlovskaya I. S., Naumavets S. N. Classical solution to the first mixed problem for one-dimensional wave equation with conditions of cauchy type. VestsіNatsyianal'naiakademііnavuk Belarusі.Seryia fіzіka-matematychnykhnavuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2015, no. 1, pp. 7–20 (in Russian).
2. Korzyuk V. I., Naumavets S. N. Classical solution of mixed problem for one-dimensional wave equation with derivatives of high order in the boundary conditions. DokladyNatsional'noiakademiinaukBelarusi= Doklady of the National Academy of Sciences of Belarus, 2016, vol. 60, no. 3, pp. 11–17 (in Russian).
3. Korzyuk V. I, Naumavets S. N., Sevastyuk V. A.On the classical solution of the second mixed problem for a one-dimensional wave equation.Trudy Institutamatematiki= Proceedings of the Institute of Mathematics, 2018, vol. 26, no. 1, pp. 35–42 (in Russian).
4. Korzyuk V. I, Naumavets S. N., Serikov V. P. The method of the characteristic parallelogram of the solution of the second mixed problem for the one-dimensional wave equation] Trudy Institutamatematiki= Proceedings of the Institute of Mathematics, 2018, vol. 26, no. 1, pp. 43–53 (in Russian).
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