Increasing Stability in the Inverse Source Problem with an Interval (<i>K</i><sub>1</sub>, <i>K</i><sub>2</sub>) of Frequencies

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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Bibliographic Details
Main Author:	Suliang Si
Format:	Article
Language:	English
Published:	MDPI AG 2025-02-01
Series:	Mathematics
Subjects:	uniqueness inverse scattering problem far-field pattern penetrable obstacle transmission problem interior transmission problem
Online Access:	https://www.mdpi.com/2227-7390/13/5/693
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Summary:	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.
ISSN:	2227-7390