Increasing Stability of The Inverse Source Problem For One Dimensional Domain
Coupled Systems of Functional Differential Equations of Fractional Orders
In this paper, we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two endpoints. Our main result is to obtain a stability estimate consists of two parts: the data discrepancy and the high frequency tail.
Aralumallige S D, Isakov V 2010 Increasing stability of the continuation for the maxwellsystemInverse Problems26074004, 14pp
Ammari H, Bao G and Fleming J 2002 Inverse source problem for Maxwell’s equationin magnetoencephalographySIAM J. Appl. Math.621369-82
Balanis C 2005Antenna Theory - Analysis and Design(Wiley, Hoboken, NJ)
Bao G, Lin J, Triki F 2010 A multi- frequency inverse source problemJ. DifferentialEquations2493443-3465.
Bao G, Lin J, Triki F 2011 An inverse source problem with multiple frequency dataComptes Rendus Mathematique349855-859.
Bao G, Lu S, Rundell W, and Xu B 2015 A recursive algorithm for multifrequencyacoustic inverse source problemsSIAM Journal on Numerical Analysis53(3), 1608-1628
Cheng J, Isakov V and Lu S 2016 Increasing stability in the inverse source problem withmany frequencies,J. Differential Equations2604786-4804
Entekhabi M N, 2018 Increasing stability in the two dimensional inverse source scatter-ing problem with attenuation and many frequenciesInverse Problems34115001
Entekhabi M N, Isakov V 2017 On increasing stability in the two dimensional inversesource scattering problem with many frequenciesInverse Problems34055005
Entekhabi M N, Gunaratne A 2019 A logarithmic estimate for inverse source scatteringproblem with attenuation in a two-layered medium, arXiv: 1903.03475 [math. AP],Tobe appeared in Applicable Analysis
Entekhabi M N, Isakov V 2018 Increasing stability in acoustic and elastic inverse sourceproblems,arXiv: 1808.10528 [math. AP],To be appeared in SIAM J MATH ANAL
Eller M and Valdivia N 2009 Acoustic source identification using multiple frequencyinformationInverse Problems25115005
Isakov V 2017Inverse Problems for Partial Differential Equations( Springer-Verlag,New York)
Isakov V, Kindermann S 2011 Regions of stability in the Cauchy problem for theHelmholtz equationMethods Appl. Anal.181-30.
Isakov V, Lu S 2018 Increasing stability in the inverse source problem with attenuationand many frequenciesTo Be Appeared in SIAM J. Appl. Math181-18
Isakov V, Lu S 2018 Inverse source problems without (pseudo)convexity assumptionsInverse Problems Imagingto appear7
John F 1982Partial Differential Equations(Applied Mathematical Sciences, Springer-Verlag, New York, Berlin) John F 1960 Continuous dependence on data for solutions of partial differential equa-tions with a prescribed boundComm. Pure Appl. Math.13551-587
Zhao Y, Li P 2017 Stability on the one-dimensional inverse source scatter-ing problem in a two-layered medium,Applicable Analysis,98:4, 682-692, DOI:10.1080/00036811.2017.1399365
Li P, Yuan G 2017 Increasing stability for the inverse source scattering problem withmulti-frequenciesInverse Problems and Imaging11745-759
Copyright (c) 2019 Manal S.I. Zaki, Hind Hashem
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.