Article
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.ru
Potekho A.O. Сandidate of Physics and Mathematics, Associate Professor, potehoao@rambler.ru
Bibliographic description
Section Scientific Research
UDK 517.982.43
DOI
Article type
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.
Key words semi-bounded string, wave equation, elastic contact, method of convolution of Fourier expansions.
Article information
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 articleSolution of a Boundary Value Problem on Semi-Bounded String Motion with the Boundary Condition of the Third Kind