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dc.contributor.authorIsakov, Victor
dc.contributor.authorLu, Shuai
dc.identifier.citationVictor Isakov, Shuai Lu. Inverse source problems without (pseudo) convexity assumptions. Inverse Problems & Imaging, 2018, 12 (4) : 955-970en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractWe study the inverse source problem for the Helmholtz equation from boundary Cauchy data with multiple wave numbers. The main goal of this paper is to study the uniqueness and increasing stability when the (pseudo)convexity or non-trapping conditions for the related hyperbolic problem are not satisfied. We consider general elliptic equations of the second order and arbitrary observation sites. To show the uniqueness we use the analytic continuation, the Fourier transform with respect to the wave numbers and uniqueness in the lateral Cauchy problem for hyperbolic equations. Numerical examples in 2 spatial dimension support the analysis and indicate the increasing stability for large intervals of the wave numbers, while analytic proofs of the increasing stability are not available.en_US
dc.description.sponsorshipEmylou Keith and Betty Dutcher Distinguished Professorship and the NSF grant DMS 15-14886. Shuai Lu is supported by NSFC No. 11522108, 91630309, Shanghai Municipal Education Commission No. 16SG01 and Special Funds for Major State Basic Research Projects of China (2015CB856003).en_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.ispartofseriesInverse Problems & Imaging;v.12:no.4
dc.subjectInverse source problemsen_US
dc.subjectMulti-frequency dataen_US
dc.subject(Pseudo) convexityen_US
dc.titleInverse source problems without (pseudo) convexity assumptionsen_US
dc.rights.holder© 2018 American Institute of Mathematical Sciencesen_US

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