Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy
In this paper, we study boundary controllability for the linear extension problem of a wave equation with space-dependent coefficients and having an internal degeneracy. For this purpose, we mainly focus on the well-posedness and the boundary null controllability of a relaxed version of the original...
Gespeichert in:
| Veröffentlicht in: | Journal of applied analysis 2024-12, Vol.30 (2), p.325-343 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 343 |
|---|---|
| container_issue | 2 |
| container_start_page | 325 |
| container_title | Journal of applied analysis |
| container_volume | 30 |
| creator | Azzaoui, Mohamed Salhi, Jawad Tilioua, Mouhcine |
| description | In this paper, we study boundary controllability for the linear extension problem of a wave equation with space-dependent coefficients and having an internal degeneracy. For this purpose, we mainly focus on the well-posedness and the boundary null controllability of a relaxed version of the original problem, namely, to some degenerate transmission problem. The key ingredient is to derive direct and inverse inequalities for the associated homogeneous degenerate adjoint problem. By these inequalities, we deduce that the transmission problem has a unique solution by transposition and this solution is null controllable. Moreover, we give an explicit formula of the controllability time. |
| doi_str_mv | 10.1515/jaa-2023-0125 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3133420887</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3133420887</sourcerecordid><originalsourceid>FETCH-LOGICAL-c273t-c7cd103c1a4777a0c41c24125b77dbeeb2bc259ae2da0b22fc242043b223603c3</originalsourceid><addsrcrecordid>eNptkEtLAzEUhYMoWKtL9wHX0TxmJlNcafEFBTe6DpnMHU2ZJm0y09J_7y0V3LhJTrjnHnI-Qq4FvxWlKO-W1jLJpWJcyPKETERdzVjFa3mKupAlq2a8PicXOS85l7Kqignxj3EMrU176mIYUux72_jeD3vaxUS3Nnnb9IBD6DrvPIQh0xiAtX4FIfsYbE93dgsUNqMd8E13fvimPgyQPCa08AUBknX7S3LW2T7D1e89JZ_PTx_zV7Z4f3mbPyyYk1oNzGnXCq6csIXW2nJXCCcLLNRo3TYAjWycLGcWZGt5I2WHU8kLhVJVuKem5OaYu05xM0IezDKOCf-ZjRJKobmuNbrY0eVSzDlBZ9bJr5CDEdwcaBqkaQ40zYEm-u-P_p3tsRrWSuMexV_4_3so8PwBOZ19eQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3133420887</pqid></control><display><type>article</type><title>Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy</title><source>Alma/SFX Local Collection</source><creator>Azzaoui, Mohamed ; Salhi, Jawad ; Tilioua, Mouhcine</creator><creatorcontrib>Azzaoui, Mohamed ; Salhi, Jawad ; Tilioua, Mouhcine</creatorcontrib><description>In this paper, we study boundary controllability for the linear extension problem of a wave equation with space-dependent coefficients and having an internal degeneracy. For this purpose, we mainly focus on the well-posedness and the boundary null controllability of a relaxed version of the original problem, namely, to some degenerate transmission problem. The key ingredient is to derive direct and inverse inequalities for the associated homogeneous degenerate adjoint problem. By these inequalities, we deduce that the transmission problem has a unique solution by transposition and this solution is null controllable. Moreover, we give an explicit formula of the controllability time.</description><identifier>ISSN: 1425-6908</identifier><identifier>EISSN: 1869-6082</identifier><identifier>DOI: 10.1515/jaa-2023-0125</identifier><language>eng</language><publisher>Berlin: De Gruyter</publisher><subject>35L80 ; 93B05 ; 93B07 ; 93C05 ; 93C20 ; Boundary controllability ; Controllability ; degenerate wave equation ; Hilbert uniqueness method ; Inequalities ; interior degeneracy ; variable coefficients ; Wave equations</subject><ispartof>Journal of applied analysis, 2024-12, Vol.30 (2), p.325-343</ispartof><rights>2024 Walter de Gruyter GmbH, Berlin/Boston</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c273t-c7cd103c1a4777a0c41c24125b77dbeeb2bc259ae2da0b22fc242043b223603c3</cites><orcidid>0000-0001-9290-9681</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Azzaoui, Mohamed</creatorcontrib><creatorcontrib>Salhi, Jawad</creatorcontrib><creatorcontrib>Tilioua, Mouhcine</creatorcontrib><title>Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy</title><title>Journal of applied analysis</title><description>In this paper, we study boundary controllability for the linear extension problem of a wave equation with space-dependent coefficients and having an internal degeneracy. For this purpose, we mainly focus on the well-posedness and the boundary null controllability of a relaxed version of the original problem, namely, to some degenerate transmission problem. The key ingredient is to derive direct and inverse inequalities for the associated homogeneous degenerate adjoint problem. By these inequalities, we deduce that the transmission problem has a unique solution by transposition and this solution is null controllable. Moreover, we give an explicit formula of the controllability time.</description><subject>35L80</subject><subject>93B05</subject><subject>93B07</subject><subject>93C05</subject><subject>93C20</subject><subject>Boundary controllability</subject><subject>Controllability</subject><subject>degenerate wave equation</subject><subject>Hilbert uniqueness method</subject><subject>Inequalities</subject><subject>interior degeneracy</subject><subject>variable coefficients</subject><subject>Wave equations</subject><issn>1425-6908</issn><issn>1869-6082</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</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>eNptkEtLAzEUhYMoWKtL9wHX0TxmJlNcafEFBTe6DpnMHU2ZJm0y09J_7y0V3LhJTrjnHnI-Qq4FvxWlKO-W1jLJpWJcyPKETERdzVjFa3mKupAlq2a8PicXOS85l7Kqignxj3EMrU176mIYUux72_jeD3vaxUS3Nnnb9IBD6DrvPIQh0xiAtX4FIfsYbE93dgsUNqMd8E13fvimPgyQPCa08AUBknX7S3LW2T7D1e89JZ_PTx_zV7Z4f3mbPyyYk1oNzGnXCq6csIXW2nJXCCcLLNRo3TYAjWycLGcWZGt5I2WHU8kLhVJVuKem5OaYu05xM0IezDKOCf-ZjRJKobmuNbrY0eVSzDlBZ9bJr5CDEdwcaBqkaQ40zYEm-u-P_p3tsRrWSuMexV_4_3so8PwBOZ19eQ</recordid><startdate>20241201</startdate><enddate>20241201</enddate><creator>Azzaoui, Mohamed</creator><creator>Salhi, Jawad</creator><creator>Tilioua, Mouhcine</creator><general>De Gruyter</general><general>Walter de Gruyter GmbH</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</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>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>L.-</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PYYUZ</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0001-9290-9681</orcidid></search><sort><creationdate>20241201</creationdate><title>Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy</title><author>Azzaoui, Mohamed ; Salhi, Jawad ; Tilioua, Mouhcine</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c273t-c7cd103c1a4777a0c41c24125b77dbeeb2bc259ae2da0b22fc242043b223603c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>35L80</topic><topic>93B05</topic><topic>93B07</topic><topic>93C05</topic><topic>93C20</topic><topic>Boundary controllability</topic><topic>Controllability</topic><topic>degenerate wave equation</topic><topic>Hilbert uniqueness method</topic><topic>Inequalities</topic><topic>interior degeneracy</topic><topic>variable coefficients</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Azzaoui, Mohamed</creatorcontrib><creatorcontrib>Salhi, Jawad</creatorcontrib><creatorcontrib>Tilioua, Mouhcine</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems 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>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>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>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>ABI/INFORM Professional Advanced</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>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>ProQuest Central China</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of applied analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Azzaoui, Mohamed</au><au>Salhi, Jawad</au><au>Tilioua, Mouhcine</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy</atitle><jtitle>Journal of applied analysis</jtitle><date>2024-12-01</date><risdate>2024</risdate><volume>30</volume><issue>2</issue><spage>325</spage><epage>343</epage><pages>325-343</pages><issn>1425-6908</issn><eissn>1869-6082</eissn><abstract>In this paper, we study boundary controllability for the linear extension problem of a wave equation with space-dependent coefficients and having an internal degeneracy. For this purpose, we mainly focus on the well-posedness and the boundary null controllability of a relaxed version of the original problem, namely, to some degenerate transmission problem. The key ingredient is to derive direct and inverse inequalities for the associated homogeneous degenerate adjoint problem. By these inequalities, we deduce that the transmission problem has a unique solution by transposition and this solution is null controllable. Moreover, we give an explicit formula of the controllability time.</abstract><cop>Berlin</cop><pub>De Gruyter</pub><doi>10.1515/jaa-2023-0125</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-9290-9681</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1425-6908 |
| ispartof | Journal of applied analysis, 2024-12, Vol.30 (2), p.325-343 |
| issn | 1425-6908 1869-6082 |
| language | eng |
| recordid | cdi_proquest_journals_3133420887 |
| source | Alma/SFX Local Collection |
| subjects | 35L80 93B05 93B07 93C05 93C20 Boundary controllability Controllability degenerate wave equation Hilbert uniqueness method Inequalities interior degeneracy variable coefficients Wave equations |
| title | Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T01%3A05%3A15IST&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=Boundary%20controllability%20for%20variable%20coefficients%20one-dimensional%20wave%20equation%20with%20interior%20degeneracy&rft.jtitle=Journal%20of%20applied%20analysis&rft.au=Azzaoui,%20Mohamed&rft.date=2024-12-01&rft.volume=30&rft.issue=2&rft.spage=325&rft.epage=343&rft.pages=325-343&rft.issn=1425-6908&rft.eissn=1869-6082&rft_id=info:doi/10.1515/jaa-2023-0125&rft_dat=%3Cproquest_cross%3E3133420887%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=3133420887&rft_id=info:pmid/&rfr_iscdi=true |