Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media
In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the bound...
Saved in:
| Published in | Journal of spectral theory Vol. 11; no. 1; pp. 1 - 38 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
European Mathematical Society Publishing House
01.01.2021
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1664-039X 1664-0403 |
| DOI | 10.4171/jst/334 |
Cover
| Abstract | In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the boundary. We are interested in the case of the time-harmonic Maxwell equations. |
|---|---|
| AbstractList | In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the boundary. We are interested in the case of the time-harmonic Maxwell equations. In the current paper we consider an inverse boundary value problem of electro-magnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of the medium by making electromagnetic measurements on the boundary. We are interested in the case of the time-harmonic Maxwell equations. Mathematics Subject Classification (2010). 35Q61, 35R30, 78A, 65M32, 65N21. Keywords. Inverse problems, nonlinear Maxwell's equations, Kerr-type media. |
| Audience | Academic |
| Author | Zhou, Ting Assylbekov, Yernat M. |
| Author_xml | – sequence: 1 givenname: Yernat M. surname: Assylbekov fullname: Assylbekov, Yernat M. – sequence: 2 givenname: Ting surname: Zhou fullname: Zhou, Ting |
| BookMark | eNplUE1PwzAMjdCQGGPiL-TGqVvapMl6nManGOIAB24lTRyWqU1HEj7278kYXEA-2H5-fpbfMRq43gFCpzmZsFzk03WIU0rZARrmnLOMMEIHvzWtno7QOIQ1ISQhIs2G6PncelARS6exde_gA-CN75sWuoBN73FcAU5HWutAps52kK2k73pnFb6Tnx_Qthhe32S0vQtJAt-C91ncbgB3oK08QYdGtgHGP3mEHi4vHhfX2fL-6mYxX2aqqETMmlkjDKOzXDRKUzKTUBleFJxoJhKhkCo3FLiptDYzqHRRlaXhXJWsZETTEZrsVV9kC7V1po9eqhQaOquSR8YmfM5LLgTdxQid7ReU70PwYOqNt5302zon9c7KOllZJysTM_vDVDZ-v5tO2PYf_wsHVXlI |
| CitedBy_id | crossref_primary_10_1088_1361_6420_ad3088 crossref_primary_10_1090_proc_16255 crossref_primary_10_1137_23M1604060 crossref_primary_10_1090_proc_16060 crossref_primary_10_1088_1361_6420_ac91ee crossref_primary_10_1088_1361_6420_ad92a1 crossref_primary_10_1137_23M1587993 |
| ContentType | Journal Article |
| Copyright | COPYRIGHT 2021 European Mathematical Society Publishing House |
| Copyright_xml | – notice: COPYRIGHT 2021 European Mathematical Society Publishing House |
| DBID | AAYXX CITATION |
| DOI | 10.4171/jst/334 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 1664-0403 |
| EndPage | 38 |
| ExternalDocumentID | A656773737 10_4171_jst_334 |
| GeographicLocations | United States |
| GeographicLocations_xml | – name: United States |
| GroupedDBID | AAYXX AENEX AKZPS ALMA_UNASSIGNED_HOLDINGS AUREJ CITATION FEDTE GROUPED_DOAJ H13 HVGLF IAO IGS ITC J9A REW VH7 AAFWJ AFPKN OK1 |
| ID | FETCH-LOGICAL-c297t-b8b7f43817bcd308ae9f62260d472972ac1f3e6f9ddf8e9d2955f66c54540d3 |
| ISSN | 1664-039X |
| IngestDate | Sat Mar 08 18:39:30 EST 2025 Thu Apr 24 22:59:30 EDT 2025 Tue Jul 01 04:21:29 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c297t-b8b7f43817bcd308ae9f62260d472972ac1f3e6f9ddf8e9d2955f66c54540d3 |
| OpenAccessLink | https://ems.press/content/serial-article-files/12124 |
| PageCount | 38 |
| ParticipantIDs | gale_infotracacademiconefile_A656773737 crossref_primary_10_4171_jst_334 crossref_citationtrail_10_4171_jst_334 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-01-01 |
| PublicationDateYYYYMMDD | 2021-01-01 |
| PublicationDate_xml | – month: 01 year: 2021 text: 2021-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of spectral theory |
| PublicationYear | 2021 |
| Publisher | European Mathematical Society Publishing House |
| Publisher_xml | – name: European Mathematical Society Publishing House |
| SSID | ssj0001667403 |
| Score | 2.3068209 |
| Snippet | In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the... In the current paper we consider an inverse boundary value problem of electro-magnetism in a nonlinear Kerr medium. We show the unique determination of the... |
| SourceID | gale crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 1 |
| SubjectTerms | Boundary value problems Differential equations, Nonlinear Mathematical research Maxwell equations |
| Title | Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media |
| Volume | 11 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1664-0403 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0001667403 issn: 1664-039X databaseCode: DOA dateStart: 20210101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwELa22wuXvgCVUiofKjggQ2I7dnxEqAi12l4AiVuwHecCYmE3W7X99Ywfm80uVLRVpCiyYivxfBrPjOabQeizkrRWtlCkKZQm3JSaaGczIpXMtCmdkYHHPfouTi_418vicjA462UtzVpzYH8_ySv5H6nCGMjVs2T_QbLdojAAzyBfuIOE4f5XMo76KhVQ8vkVnvUUGsRMu_TB21gLQ09CG3niK1WHpjcj_TPE7dz9bJFP_s1NJiREZQOj5A-Wa2BnemJ_Oyf2R8xMp79ujLse_wh6PQQa90cHi9D0eBbRkQ7LFGugeS_WENWjEJxkLDS_hdOjN8YztqRT80fYiQoy7520sazLqg7nuQw63FNeTliKdC7VyV45v7qsQvBn_OQKplYw8QV6SaUQtOdnh8CbEJKHjtnd30QytZ97CHMPGeNLVspwnieZrI7zN-hV2nR8FGX_Fg3c7Tv0OrkOOCnm6Tq6ilDAAAWcoIDnUMAABQyiwh0U8BIUcIIC7qAAS-AOCjhAYQOdnXw5Pz4lqXkGsVTJlpjSyMbXb5PG1iwrtVONAFs7qzn4U5JqmzfMiUbVdVM6VVNVFI0QtvAlGWu2iYbwUe49woUDkxlGGTWMy8yWMGBskytrwVikdgvtzreqsqmuvG9vclOtyGML4e7Fu1hK5fEre36vK48HWMPqxBGBL_Flyqoj8D6kZHB9eH6xbbS2wPBHNGwnM7cDFmRrPgVEPACCHXcw |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Direct+and+inverse+problems+for+the+nonlinear+time-harmonic+Maxwell+equations+in+Kerr-type+media&rft.jtitle=Journal+of+spectral+theory&rft.au=Assylbekov%2C+Yernat+M.&rft.au=Zhou%2C+Ting&rft.date=2021-01-01&rft.issn=1664-039X&rft.eissn=1664-0403&rft.volume=11&rft.issue=1&rft.spage=1&rft.epage=38&rft_id=info:doi/10.4171%2Fjst%2F334&rft.externalDBID=n%2Fa&rft.externalDocID=10_4171_jst_334 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1664-039X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1664-039X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1664-039X&client=summon |