О периодических решениях волновых уравнений второго порядка
It is established that the linear problem utt−a²uxx=g(x,t), u(0,t)=u(π,t), u(x,t+T)=u(x,t) is always solvable in the space of functions A={g:g(x,t)=g(x,t+T)=g(π−x,t)=−g(−x,t)} provided that aTq=(2p−1)π, (2p−1,q)=1, where p,q are integers. To prove this statement, an explicit solution is constructed...
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| Published in: | Український математичний журнал |
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| Date: | 1993 |
| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Інститут математики НАН України
1993
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| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155009 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | О периодических решениях волновых уравнений второго порядка / Ю.А. Митропольський, Г.П. Хома // Український математичний журнал. — 1993. — Т. 45, № 8. — С. 1115–1121. — Бібліогр.: 7 назв. — рос. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | It is established that the linear problem utt−a²uxx=g(x,t), u(0,t)=u(π,t), u(x,t+T)=u(x,t) is always solvable in the space of functions A={g:g(x,t)=g(x,t+T)=g(π−x,t)=−g(−x,t)} provided that aTq=(2p−1)π, (2p−1,q)=1, where p,q are integers. To prove this statement, an explicit solution is constructed in the form of an integral operator which is used to prove the existence of a solution to aperiodic boundary value problem for nonlinear second order wave equation. The results obtained can be employed in the study of solutions to nonlinear boundary value problems by asymptotic methods.
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| ISSN: | 1027-3190 |