Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity
A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method u...
Gespeichert in:
| Veröffentlicht in: | Computational mathematics and mathematical physics 2018-09, Vol.58 (9), p.1531-1543 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1543 |
|---|---|
| container_issue | 9 |
| container_start_page | 1531 |
| container_title | Computational mathematics and mathematical physics |
| container_volume | 58 |
| creator | Khromov, A. P. |
| description | A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found. |
| doi_str_mv | 10.1134/S0965542518090099 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2120593374</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2120593374</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-f1df420157a4aa331da83416cf08b2e8eabd00ba32553276c6ee545babfd9e513</originalsourceid><addsrcrecordid>eNp1kEtLw0AUhQdRsFZ_gLsB19F5N7OUUm2hVcHXMkySO3VKkmlnErX-elMquBBXd3G-71w4CJ1TckkpF1ePRCspBZM0JZoQrQ_QgEopE6UUO0SDXZzs8mN0EuOKEKp0ygdosXCfUOKH4PMKamx9wAZPfe2X0IDvIn4174Anm860zjf4w7VvPXDnmy8IHs8a1zpT4ReofOHa7Sk6sqaKcPZzh-j5ZvI0nibz-9vZ-HqeFEylbWJpaQUjVI6MMIZzWpqUC6oKS9KcQQomLwnJDWdScjZShQKQQuYmt6UGSfkQXex718FvOohttvJdaPqXGaOMSM35SPQU3VNF8DEGsNk6uNqEbUZJtlst-7Na77C9E3u2WUL4bf5f-gbijm4L</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2120593374</pqid></control><display><type>article</type><title>Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity</title><source>Springer Nature - Complete Springer Journals</source><creator>Khromov, A. P.</creator><creatorcontrib>Khromov, A. P.</creatorcontrib><description>A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.</description><identifier>ISSN: 0965-5425</identifier><identifier>EISSN: 1555-6662</identifier><identifier>DOI: 10.1134/S0965542518090099</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Computational Mathematics and Numerical Analysis ; Fourier series ; Mathematics ; Mathematics and Statistics ; Smoothness ; Velocity ; Wave equations</subject><ispartof>Computational mathematics and mathematical physics, 2018-09, Vol.58 (9), p.1531-1543</ispartof><rights>Pleiades Publishing, Ltd. 2018</rights><rights>Computational Mathematics and Mathematical Physics is a copyright of Springer, (2018). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-f1df420157a4aa331da83416cf08b2e8eabd00ba32553276c6ee545babfd9e513</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0965542518090099$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0965542518090099$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Khromov, A. P.</creatorcontrib><title>Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity</title><title>Computational mathematics and mathematical physics</title><addtitle>Comput. Math. and Math. Phys</addtitle><description>A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.</description><subject>Computational Mathematics and Numerical Analysis</subject><subject>Fourier series</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Smoothness</subject><subject>Velocity</subject><subject>Wave equations</subject><issn>0965-5425</issn><issn>1555-6662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEtLw0AUhQdRsFZ_gLsB19F5N7OUUm2hVcHXMkySO3VKkmlnErX-elMquBBXd3G-71w4CJ1TckkpF1ePRCspBZM0JZoQrQ_QgEopE6UUO0SDXZzs8mN0EuOKEKp0ygdosXCfUOKH4PMKamx9wAZPfe2X0IDvIn4174Anm860zjf4w7VvPXDnmy8IHs8a1zpT4ReofOHa7Sk6sqaKcPZzh-j5ZvI0nibz-9vZ-HqeFEylbWJpaQUjVI6MMIZzWpqUC6oKS9KcQQomLwnJDWdScjZShQKQQuYmt6UGSfkQXex718FvOohttvJdaPqXGaOMSM35SPQU3VNF8DEGsNk6uNqEbUZJtlst-7Na77C9E3u2WUL4bf5f-gbijm4L</recordid><startdate>20180901</startdate><enddate>20180901</enddate><creator>Khromov, A. P.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20180901</creationdate><title>Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity</title><author>Khromov, A. P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-f1df420157a4aa331da83416cf08b2e8eabd00ba32553276c6ee545babfd9e513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Computational Mathematics and Numerical Analysis</topic><topic>Fourier series</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Smoothness</topic><topic>Velocity</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khromov, A. P.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Computational mathematics and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khromov, A. P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity</atitle><jtitle>Computational mathematics and mathematical physics</jtitle><stitle>Comput. Math. and Math. Phys</stitle><date>2018-09-01</date><risdate>2018</risdate><volume>58</volume><issue>9</issue><spage>1531</spage><epage>1543</epage><pages>1531-1543</pages><issn>0965-5425</issn><eissn>1555-6662</eissn><abstract>A mixed problem for a homogeneous wave equation with fixed ends, a summable potential, and a nonzero initial velocity is studied. Using the resolvent approach and developing the Krylov method for accelerating the convergence of Fourier series, a classical solution is obtained by the Fourier method under minimal conditions on the smoothness of the initial data and a generalized solution in the case of the initial velocity represented by an arbitrary summable function is found.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0965542518090099</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0965-5425 |
| ispartof | Computational mathematics and mathematical physics, 2018-09, Vol.58 (9), p.1531-1543 |
| issn | 0965-5425 1555-6662 |
| language | eng |
| recordid | cdi_proquest_journals_2120593374 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Computational Mathematics and Numerical Analysis Fourier series Mathematics Mathematics and Statistics Smoothness Velocity Wave equations |
| title | Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T03%3A12%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Mixed%20Problem%20for%20a%20Homogeneous%20Wave%20Equation%20with%20a%20Nonzero%20Initial%20Velocity&rft.jtitle=Computational%20mathematics%20and%20mathematical%20physics&rft.au=Khromov,%20A.%20P.&rft.date=2018-09-01&rft.volume=58&rft.issue=9&rft.spage=1531&rft.epage=1543&rft.pages=1531-1543&rft.issn=0965-5425&rft.eissn=1555-6662&rft_id=info:doi/10.1134/S0965542518090099&rft_dat=%3Cproquest_cross%3E2120593374%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2120593374&rft_id=info:pmid/&rfr_iscdi=true |