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A PROBLEM ON VIBRATION OF A BAR WITH UNKNOWN BOUNDARY CONDITION ON A PART OF THE BOUNDARY
- Authors: Beylin A.B.1, Pulkina L.S.2
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Affiliations:
- Samara State Technical University
- Samara National Research University
- Issue: Vol 23, No 2 (2017)
- Pages: 7-14
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5147
- DOI: https://doi.org/10.18287/2541-7525-2017-23-2-7-14
- ID: 5147
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Abstract
In this paper, we study an inverse problem for hyperbolic equation. This problem arises when we consider vibration of a nonhomogeneous bar if one endpoint is fixed by spring but behavior of the other is unknown and is the subject to find. Overdetermination is given in the form of integral with respect to spacial variable. Unique solvability of this problem is proved under some conditions on data. The proof is based on a priori estimates in Sobolev space.
About the authors
A. B. Beylin
Samara State Technical University
Author for correspondence.
Email: morenov@ssau.ru
Russian Federation
L. S. Pulkina
Samara National Research University
Email: morenov@ssau.ru
Russian Federation
References
- Babakov I.M. Teoriia kolebanii . M.: Nauka, 1968, 560 p. .
- Birger I.A., Shorr B.F., Iosilevich G.B. Raschet na prochnost’ detalei mashin: Spravochnik . M.: Mashinostroenie, 1993, 640 p. .
- Khazanov Kh.S. Mekhanicheskie kolebaniia sistem s raspredelennymi parametrami: ucheb. posobie . Samara, Samar. Gosud. Aerokosmich. Un-t, 2002, 80 p. .
- Veitz V.L., Dondoshanskii V.K., Chiriaev V.I. Vynuzhdennye kolebaniia v metallorezhushchikh stankakh . M-L.: Mashgiz, 1959, 288 p. .
- Kumabe D. Vibratsionnoe rezanie . M.: Mashinostroenie, 1985, 424 p. .
- Rao J.S. Advanced Theory of Vibration. N.Y.: Wiley, 1992, 431 p. .
- Fedotov I.A., Polyanin A.D., Shatalov M.Yu. Teoriia svobodnykh i vynuzhdennykh kolebanii tverdogo sterzhnia, osnovannaia na modeli Releia . Doklady RAN , 2007, Vol. 417, no. 1, pp. 56–61 .
- Beylin A.B., Pulkina L.S. Zadacha o prodol’nykh kolebaniiakh sterzhnia s dinamicheskimi granichnymi usloviiami . Vestnik SamGU. Estestvennonauchnaia seriia , 2014, no. 3(114), pp. 9–19.
- Beylin A.B. Zadacha o prodol’nykh kolebaniiakh uprugo zakreplennogo nagruzhennogo sterzhnia . Vestnik Samarskogo gos. Tekh. Un-ta. Seriia: Fiz.-mat. nauki , 2016, Vol. 20, no. 2, pp. 249–258 .
- Prilepko A.I., Kostin A.B. Ob obratnykh zadachakh opredeleniia koeffitsienta v parabolicheskom uravnenii. II . Sibirskii mat. zhurnal , 1993, Vol. 34, no. 5 .
- Kamynin V.L. Obratnaia zadacha opredeleniia mladshego koeffitsienta v parabolicheskom uravnenii pri uslovii integral’nogo nabliudeniia . Matem. zametki , 2013, 94,(2), pp. 205–213 .
- Cannon J.R., Lin Y. Determination of a parameter p(t) in some quasi-linear parabolic differential equations. Inverse Problems, 1988, no. 4, pp. 35–45 .
- Denisov A.M. Obratnaia zadacha dlia giperbolicheskogo uravneniia s nelokal’nym kraevym usloviem, soderzhashchim zapazdyvaiushchii argument . Trudy instituta matematiki i mekhaniki UrO RAN , 2012, Vol. 18, No. 1 .
- Ladyzhenskaya O.A. Kraevye zadachi matematicheskoi fiziki . M.: Nauka, 1973 .
- Pulkina L.S. Kraevye zadachi dlia giperbolicheskogo uravneniia s nelokal’nymi usloviiami I i II roda . Izvestiia vuzov. Matematika , 2012, no. 4, pp. 74–83 .
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