Phaseless Inverse Problems for Schrödinger, Helmholtz, and Maxwell Equations
A survey of recent research concerning phaseless inverse problems for several differential equations is given. Mainly, the surveyed studies were performed over the last five years, although their importance of this subject for quantum scattering theory was noted more than 40 years ago. Problem formu...
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| Published in | Computational mathematics and mathematical physics Vol. 60; no. 6; pp. 1045 - 1062 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.06.2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0965-5425 1555-6662 |
| DOI | 10.1134/S0965542520060093 |
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| Abstract | A survey of recent research concerning phaseless inverse problems for several differential equations is given. Mainly, the surveyed studies were performed over the last five years, although their importance of this subject for quantum scattering theory was noted more than 40 years ago. Problem formulations and results are presented, and the basic ideas underlying the research are described. |
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| AbstractList | A survey of recent research concerning phaseless inverse problems for several differential equations is given. Mainly, the surveyed studies were performed over the last five years, although their importance of this subject for quantum scattering theory was noted more than 40 years ago. Problem formulations and results are presented, and the basic ideas underlying the research are described. |
| Author | Romanov, V. G. |
| Author_xml | – sequence: 1 givenname: V. G. surname: Romanov fullname: Romanov, V. G. email: romanov@math.nsc.ru organization: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences |
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| Cites_doi | 10.1016/j.jcp.2011.01.038 10.1137/130926250 10.1007/978-1-4899-6765-7 10.1190/1.1437915 10.1137/1.9780898719284 10.1016/j.apnum.2016.08.014 10.1137/15M1043959 10.1007/BF01660580 10.1070/RM1966v021n03ABEH004157 10.1007/978-3-642-83671-8 10.1088/0266-5611/14/2/001 10.1023/B:SIMJ.0000048926.66814.81 10.1063/1.529990 10.1007/978-3-662-12125-2 10.1088/1361-6420/aa7a18 10.1088/0266-5611/32/1/015005 10.1515/9783110943849 10.1016/j.physleta.2011.01.052 10.1137/15M1022367 10.3934/ipi.2019005 10.1134/S1064562419010137 10.1007/5.12220-014-9553-7 10.1134/S1064562417030164 10.1007/978-1-4419-7805-9 10.1016/j.wavemoti.2012.04.008 10.1134/S1064562419050168 10.1016/j.aml.2014.06.005 10.1515/jiip-2018-0037 10.1134/S1990478919030050 10.1021/la802779r 10.1515/jiip-2015-0025 10.1134/S1990478918030079 10.1515/9783110926019 10.1080/00036811.2013.818136 10.1016/0041-5553(65)90157-6 10.3934/ipi.2017013 10.1364/JOSAA.30.000293 10.1134/S1064562411040247 10.1134/S0037446618030126 10.1134/S0037446611040124 10.1016/j.bulsci.2015.04.005 10.1134/S0037446617040176 10.1016/0040-1951(73)90095-4 10.1134/S0037446619040116 |
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| Keywords | Helmholtz equation inverse kinematic problem tomography Schrödinger equation phaseless inverse problems Maxwell’s equations |
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Tikhonov (1361_CR54) 1950; 73 V. G. Romanov (1361_CR60) 2004; 45 V. G. Romanov (1361_CR67) 2019; 60 1361_CR13 A. S. Alekseev (1361_CR36) 1973; 20 M. V. Klibanov (1361_CR10) 2014; 93 V. G. Romanov (1361_CR43) 2019; 13 V. G. Romanov (1361_CR64) 1984; 2 M. V. Klibanov (1361_CR9) 2014; 37 V. G. Romanov (1361_CR65) 1984; 5 M. V. Klibanov (1361_CR44) 2017; 33 S. Helgason (1361_CR17) 1980 M. V. Klibanov (1361_CR30) 2016; 76 V. A. Dedok (1361_CR69) 2019; 13 K. Chadan (1361_CR1) 1977 V. G. Romanov (1361_CR62) 2011; 52 V. G. Romanov (1361_CR51) 2019; 100 L. Beilina (1361_CR29) 2012 R. G. Newton (1361_CR2) 1989 M. V. Klibanov (1361_CR12) 2015; 3 I. N. Bernshtein (1361_CR40) 1978; 243 cr-split#-1361_CR20.2 cr-split#-1361_CR20.1 A. N. Tikhonov (1361_CR55) 1965; 5 A. N. Tikhonov (1361_CR52) 1946; 10 V. G. Romanov (1361_CR58) 2002; 66 R. G. Mukhometov (1361_CR39) 1978; 243 R. G. Novikov (1361_CR14) 2015; 139 M. V. Klibanov (1361_CR31) 2016; 32 V. G. Romanov (1361_CR48) 2017; 95 B. R. Vainberg (1361_CR22) 1966; 21 H. Liu (1361_CR25) 2017; 32 M. V. Klibanov (1361_CR45) 2017; 11 R. G. Mukhometov (1361_CR38) 1977; 232 J. Radon (1361_CR16) 1917; 29 V. G. Romanov (1361_CR50) 2019; 99 F. Natterer (1361_CR18) 2001 R. G. Novikov (1361_CR24) 2011; 375 A. L. Karchevsky (1361_CR68) 2018; 12 N. F. Berk (1361_CR4) 2009; 25 G. Bao (1361_CR28) 2013; 30 T. Aktosun (1361_CR3) 1988; 14 V. G. Romanov (1361_CR57) 1991 V. G. Romanov (1361_CR19) 1972 V. G. Romanov (1361_CR63) 2011; 84 V. G. Romanov (1361_CR32) 2015; 3 V. G. Romanov (1361_CR46) 2018; 26 L. Cagniard (1361_CR56) 1953; 187 Z. T. Nazarchuk (1361_CR5) 2012; 49 A. N. Tikhonov (1361_CR53) 1949; 60 M. V. Klibanov (1361_CR26) 2016; 110 V. G. Romanov (1361_CR61) 2005; 71 V. G. Romanov (1361_CR66) 1986; 22 V. G. Romanov (1361_CR47) 2017; 58 O. Ivanyshyn (1361_CR6) 2011; 230 G. Herglotz (1361_CR33) 1905; 52 1361_CR21 G. Ya. Beil’kin (1361_CR41) 1983; 21 M. V. Klibanov (1361_CR7) 1992; 33 V. G. Romanov (1361_CR59) 2003; 67 V. G. Romanov (1361_CR49) 2018; 59 V. G. Romanov (1361_CR34) 1967; 8 M. V. Klibanov (1361_CR8) 2014; 74 M. V. Klibanov (1361_CR11) 2015; 23 A. S. Alekseev (1361_CR35) 1969 R. G. Novikov (1361_CR15) 2015; 3 H. Ammari (1361_CR27) 2016; 76 |
| References_xml | – reference: KlibanovM. V.Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-dAppl. Anal.2014931135114931958781301.35214 – reference: NovikovR. G.Phaseless inverse scattering in the one-dimensional caseEurasian J. Math. Comput. Appl.201536470 – reference: RomanovV. G.Inverse Problems for Hyperbolic Equations1972NovosibirskNauka – reference: RomanovV. G.Problem of determining the permittivity in the stationary system of Maxwell equationsDokl. Math.20179523023437535341375.35532 – reference: LiuH.WangY.Recovering an electromagnetic obstacle by a few phaseless backscattering measurementsInverse Probl.2017320350136268161432.78008 – reference: NewtonR. G.Inverse Schrodinger Scattering in Three Dimensions1989New YorkSpringer0697.35005 – reference: RomanovV. G.Stability estimate of a solution to the problem of kernel determination in integrodifferential equations of electrodynamicsDokl. 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| Title | Phaseless Inverse Problems for Schrödinger, Helmholtz, and Maxwell Equations |
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