Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies
In this paper, we study the increasing stability in the inverse source problem with an interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>K</mi><m...
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2025-02-01
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| author | Suliang Si |
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| description | In this paper, we study the increasing stability in the inverse source problem with an interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>K</mi><mn>1</mn></msub><mo>,</mo><msub><mi>K</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> of frequencies. Our results show that increasing stability can be obtained with larger wavenumber intervals. The stability estimate consists of the Lipschitz type data discrepancy and the frequency tail of the source function, where the latter decreases as the frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>2</mn></msub></semantics></math></inline-formula> increases or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>1</mn></msub></semantics></math></inline-formula> decreases. The method is based on the Fourier transform and explicit bounds for analytic continuation. |
| format | Article |
| id | doaj-art-e4e5d0ce0580421f8fe91eab39bff504 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-e4e5d0ce0580421f8fe91eab39bff5042025-08-20T02:52:41ZengMDPI AGMathematics2227-73902025-02-0113569310.3390/math13050693Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of FrequenciesSuliang Si0School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaIn this paper, we study the increasing stability in the inverse source problem with an interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>K</mi><mn>1</mn></msub><mo>,</mo><msub><mi>K</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula> of frequencies. Our results show that increasing stability can be obtained with larger wavenumber intervals. The stability estimate consists of the Lipschitz type data discrepancy and the frequency tail of the source function, where the latter decreases as the frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>2</mn></msub></semantics></math></inline-formula> increases or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mn>1</mn></msub></semantics></math></inline-formula> decreases. The method is based on the Fourier transform and explicit bounds for analytic continuation.https://www.mdpi.com/2227-7390/13/5/693uniquenessinverse scattering problemfar-field patternpenetrable obstacletransmission probleminterior transmission problem |
| spellingShingle | Suliang Si Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies Mathematics uniqueness inverse scattering problem far-field pattern penetrable obstacle transmission problem interior transmission problem |
| title | Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies |
| title_full | Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies |
| title_fullStr | Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies |
| title_full_unstemmed | Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies |
| title_short | Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies |
| title_sort | increasing stability in the inverse source problem with an interval i k i sub 1 sub i k i sub 2 sub of frequencies |
| topic | uniqueness inverse scattering problem far-field pattern penetrable obstacle transmission problem interior transmission problem |
| url | https://www.mdpi.com/2227-7390/13/5/693 |
| work_keys_str_mv | AT suliangsi increasingstabilityintheinversesourceproblemwithanintervalikisub1subikisub2suboffrequencies |