| Article |
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| Article name |
Solution of a Boundary Value Problem on Semi-Bounded String Motion with the Boundary Condition of the Third Kind |
| Authors |
Kholodovsky S.Y.Doctor of Physics and Mathematics hol47@yandex.ruPotekho A.O.Сandidate of Physics and Mathematics, Associate Professor potehoao@rambler.ru |
| Bibliographic description |
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| Section |
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| DOI |
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| UDK |
517.982.43 |
| Article type |
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| Annotation |
The paper considers the boundary problem of motion of semi-bounded string with the free
end operated by an elastic force, which is proportional to the displacement of the spring type.
With the help of the method of convolution of Fourier expansions, solution of the problem is
expressed in explicit form by means of the classical Cauchy problem solution for an unbounded
string. In limiting cases, the obtained solutions result in the solutions of classical problems
for semi-bounded strings with a free and a fixed end point.
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| Key words |
semi-bounded string, wave equation, elastic contact, method of convolution of
Fourier expansions. |
| Article information |
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| References |
1. Kholodovsky S. Ye. Metod svyortyvaniya razlozheny Furye. Sluchay obobshchyonnykh
uslovy sopryazheniya tipa treshchin (zavesy)v kusochno-neodnorodnykh sredakh // Differents.
uravneniya. 2009. T. 45. № 6. S. 855–859.
2. Kholodovsky S. Ye.Metod svyortyvaniya razlozheny Furye. Sluchay treshchin (zavesy)v
kusochno-neodnorodnom prostranstvakh // Differents. uravneniya. 2009. T. 45. № 8. S. 1204–
1208.
3. Tikhonov A. N., Samarsky A. A. Uravneniya matematicheskoy fiziki. M.: Nauka, 1972. |
| Full article | Solution of a Boundary Value Problem on Semi-Bounded String Motion with the Boundary Condition of the Third Kind |
