2025-02-23T00:20:01-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-155009%22&qt=morelikethis&rows=5
2025-02-23T00:20:01-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-155009%22&qt=morelikethis&rows=5
2025-02-23T00:20:01-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-23T00:20:01-05:00 DEBUG: Deserialized SOLR response
О периодических решениях волновых уравнений второго порядка

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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Bibliographic Details
Main Authors: Митропольський, Ю.А., Хома, Г.П.
Format: Article
Language:Russian
Published: Інститут математики НАН України 1993
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/155009
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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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