{"title":"离散赫尔姆霍兹方程的反源问题","authors":"Roman Novikov, Basant Lal Sharma","doi":"10.1088/1361-6420/ad7054","DOIUrl":null,"url":null,"abstract":"We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice <inline-formula>\n<tex-math><?CDATA $\\mathbb{Z}^d$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"ipad7054ieqn1.gif\"></inline-graphic></inline-formula>, <inline-formula>\n<tex-math><?CDATA $d \\unicode{x2A7E} 1$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>d</mml:mi><mml:mtext>⩾</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"ipad7054ieqn2.gif\"></inline-graphic></inline-formula>. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverse source problem for discrete Helmholtz equation\",\"authors\":\"Roman Novikov, Basant Lal Sharma\",\"doi\":\"10.1088/1361-6420/ad7054\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice <inline-formula>\\n<tex-math><?CDATA $\\\\mathbb{Z}^d$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">Z</mml:mi></mml:mrow><mml:mi>d</mml:mi></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\\\"ipad7054ieqn1.gif\\\"></inline-graphic></inline-formula>, <inline-formula>\\n<tex-math><?CDATA $d \\\\unicode{x2A7E} 1$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>d</mml:mi><mml:mtext>⩾</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"ipad7054ieqn2.gif\\\"></inline-graphic></inline-formula>. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6420/ad7054\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6420/ad7054","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Inverse source problem for discrete Helmholtz equation
We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Zd, d⩾1. We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.
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