Publications

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1. The uniqueness of a solution of the inverse contact problem of the logarithmic potential theory, Differential Equations, 7 (1971), 29-34.

2. Uniqueness of the solution of the inverse contact problem in potential theory, Differential Equations, 8 (1972), 21-29.

3. The inverse problem of the potential theory for the vibrating string equation, Differential Equations, 9 (1973), 55-63.

4. On the solvability of an inverse problem in potential theory, Sibirsk. Mat.Z., 14 (1973), 987-1005.

5. On the solvability of an inverse problem in potential theory, Soviet Math. Dokl., 14 (1973), 1701-1705.

6. The uniqueness of solutions of certain inverse hyperbolic problems, Differential Equations, 10 (1974), 121-123.

7. On the uniqueness of the recovery of the domain and its density from their exterior potential, Siberian Math.J., 15 (1974), 488-490.

8. Inverse theorems about the smoothness of potentials, Differential Equations, 11 (1975), 50-57.

9. Analyticity of solutions of non-linear transmission problems, Differential Equations, 12 (1976), 41-48.

10. Uniqueness theorems for inverse problems of thermal potentials, Siberian Math.J., 17 (1976), 202-212.

11. On the recovery of a domain from scattering data, Soviet Math. Dokl.,17 (1976), 1338-1340.

12. General diffraction problems for hyperbolic equations, Trudy Seminara Soboleva, 2 (1977), Novosibirsk.

13. The inverse problem of potential theory for hyperbolic equations, Differential Equations, 13 (1977), 212-218.

14. On the inverse problem of potential theory for hyperbolic equations, Soviet Math.Dokl., 18 (1977), 1411-1414.

15. Uniqueness theorems for inverse problems of potential theory, Soviet Math. Dokl., 19 (1978), 630-633.

16. On the existence of solutions of inverse problems of potential theory, Soviet Math. Dokl., 19 (1978), 673-676.

17. On recovery of a domain from scattering data, "Direct and Inverse Problems for partial differential equations and their applications", FAN, Tashkent, 1978, 148-159.

18. On regularity of boundaries of some domains, Trudy Vsesouznoj Conferenzii on Partial Differential Equations, Moscow,1978, 318.

19. On uniqueness of solutions for inverse problems of potential theory, "Inverse and Improperly Posed Problems in Differential Equations", Math. Research, B. I, Akademie-Verlag, Berlin, 1979, 135-139.

20. Strictly hyperbolic diffraction problems, Differential Equations, 16 (1978), 21-28.

21. On the uniqueness of a solution of the inverse problem of potential theory, Soviet Math. Dokl., 20 (1979), 387-390.

22. On the existence of solutions of inverse problems of potential theory, Differential Equations, 16 (1980), 694-702.

23. On the uniqueness of the solution of the Cauchy problem, Soviet Math. Dokl., 22 (1980), 694-702.

24. On recovering a potential from the modulo of gradient, Dokl. Akad. Nauk Ukr.SSR, Ser.B.,1 (1981),35-37.

25. On a class of inverse problems for parabolic equations, Soviet Math.Dokl.,25 (1982), 519-521.

26. An inverse problem for a parabolic equation, Uspehi Mat. Nauk, 37 (1982),108.

27. On the uniqueness of the continuation of solutions to hyperbolic equations, Math.Notes, 32 (1982), 517-520.

28. A Nonhyperbolic Cauchy problem for �� and its applications to Elasticity Theory, Comm.Pure Appl. Math., 39 (1986), 747-769.

29. On uniqueness of recovery of a discontinuous conductivity coefficient, Comm. Pure Appl. Math., 41 (1988), 865-877.

30. Uniqueness of the continuation across a time-like hyperplane and related inverse problems for hyperbolic equations, Comm. Part.Diff.Equat.,14 (1989), 465-478.

31. Uniqueness for inverse parabolic problems with a lateral overdetermination, Comm. Part.Diff.Equat.,14 (1989), 681-690.

32. (with A.Friedman) On the uniqueness in the inverse conductivity problem with one measurement, Indiana Univ.Math.J., 38 (1989), 563-579.

33. (with J.Powell) On the inverse conductivity problem with one measurement Inverse Problems, 5 (1990), 311-318.

34. On uniqueness in the inverse transmission scattering problem, Comm. Part. Diff.Equat., 15 (1990), 1565-1587.

35. (with K.Ames) An explicit stability estimate for an ill-posed Cauchy problem for the wave equation, J. of Math.Anal. and Appl., 156 (1991), 597-610.

36. Inverse parabolic problems with the final overdetermination, Comm.Pure Appl. Math., 54 (1991), 185-209.

37. Completeness of products of solutions and some inverse problems for PDE, J. of Diff.Equat.,92 (1991), 305-317.

38. An inverse hyperbolic problem with many boundary measurements, Comm. Part.Diff.Equat., 16 (1991), 1183-1195.

39. (with H.Bellout, A.Friedman) Stability for an inverse problem in potential theory, Trans. of AMS ,332 (1992), 271-296.

40. Stability estimates for obstacles in inverse scattering, J.of Compt. and Appl. Math., 42 (1992), 79-89.

41. (with H.Engl) On the Identifiability of Steel Reinforcement Bars in Concrete from Magnostatic Measurements, European J.of Appl.Math, 3(1992),255-262.

42. (with Z.Sun) Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8 (1992), 193-206.

43. Carleman estimates in an isotropic case and applications, J. of Diff.Equat., 105 (1993), 217-239.

44. On uniqueness in inverse problems for quasilinear parabolic equations, Arch. Rat.Mech.Anal., 124 (1993), 1-13.

45. New stability results for soft obstacles in inverse scattering, Inverse problems, 9 (1993), 535-543.

46. (with J.Sylvester) Global uniqueness for a semilinear elliptic inverse problem, Comm.Pure Appl.Math., 47 (1994), 1403-1410.

47. Uniqueness and Stability in Multidimensional Inverse Problems, Inverse Problems, 9 (1993), 579-621.

48. (with Z.Sun) The Inverse Scattering at Fixed Energies in Two Dimensions, Indiana Univ. Math.J., Indiana Univ. Math. J., 44 (1995), 883-896.

49. On uniqueness for a discontinuity surface of a speed of propagation, J. of Inverse and Ill-Posed Problems, 4 (1996),

50. (with G.Alessandrini, J.Powell) Local Uniqueness in the Inverse Conductivity Problem with One Measurement, Trans. of AMS ,347(1995),3031-3041.

51. (with A.Elcrat, O.Neculoiu) On finding a surface crack from boundary measurements, Inverse Problems, 11 (1995), 343-351.

52. (with A.Nachman) Global Uniqueness for a two-dimensional elliptic inverse problem, Trans. of AMS, 347 (1995), 3375-3391.

53. (with G.Alessandrini) Analyticity and Uniqueness for the Inverse Conductivity Problem, Rendiconti dell'Istituto di Mat. dell' Universita di Trieste, XXVII (1996), 351-369 .

54. On uniqueness in the inverse conductivity problem with one boundary measurement, Lect. in Appl. Math., Vol.30 (1994), AMS, 105-114.

55. Uniqueness and Stability in Inverse Parabolic Problems, Proc. of GAMM- SIAM Conference on "Inverse Problems in Diffusion Processes", June 27-July 1, 1994, St.Wolfgang, Oesterreich. SIAM, Philadelphia, 1995.

56. (with A. Sever) Numerical implementation of an integral equation method for the inverse conductivity problem, Inverse Problems, 12(1996), 1-13.

57. (with A.Elayyan) On uniqueness of recovery of the discontinuous conductivity coefficient of a parabolic equation, SIAM J. Math. Anal., 28(1997), 49-60.

58. On uniqueness in a lateral Cauchy problem with multiple characteristics, J. Diff. Equat., 143 (1997), 134-148.

59. (with A.Elayyan) On an Inverse Diffusion Problem, SIAM J. Appl. Math.,57 (1997), 1737-1748.

60. On reconstruction of the diffusion and of the principal coefficient of a hyperbolic equation, Proc of the IMA workshop "Inverse problems in wave propagation", March 1995,IMA Series, Vol.90, Springer-Verlag, 1997, pp. 259-277.

61. On uniqueness and stability in the Cauchy Problem, in Proceedings from the 1996 Joint Summer Research Conference, June 16-20, 1996, Mount Holyoke College, Contemporary Math., Vol. 209, AMS, Providence, R.I., 1997, pp.131-147.

62. (with A.Bukhgeim, G.V.Dyatlov) Stability of memory reconstruction from the Dirichlet-to-Neumann operator, Sib. Math. J., 38 (1997), 636-646.

63. (with I.Bouchouev) The inverse problem of option pricing, Inverse Problems, 13(1997), L11-L17.

64. (with M.Eller, G.Nakamura, D.Tataru) Uniqueness and Stability in the Cauchy Problem for Maxwell' and elasticity systems, "Nonlinear Partial Differential Equations and Their Applications", College de France Seminar, Vol. 14. Eds. D. Gioranescu, J.-L. Lions, "Studies in Mathematics and Applications" , Vol. 31, North-Holland, Elsevier Science (2002), 329-351.

65. On the uniqueness of the continuation for the von Karman system, J. Inv. Ill-Posed Problems (in print).

66. Some inverse problems for the diffusion equation, Inverse Problems, 15(1999), 3-11.

67. On uniqueness of the continuation for the thermoelasticity system, SIAM J. Math. Anal.,33 (2001), 509-522.

68. (with I. Bouchouev) Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets, Inverse Problems, 15 (1999), R1-R22.

69. (with S. Kindermann) Identification of the diffusion coefficient in a one-dimensional parabolic equation, Inverse Problems, 16 (2000), 665-681.

70. Recent results on inverse parabolic problems, Lectures at the Kyoto University, 68 pp., January 1999, to be published by the Mathematical Society of Japan.

71. (with M.Belishev, L.Pestov, V. Sharafutdinov) On reconstruction of gravity field via external electromagnetic measurements, Dokl. RAN, 372 (2000), 298-300.

72. (with M.Eller) Carleman estimates with two large parameters and applications, Proceedings of the conference "Differential-Geometric Methods in the Control of Partial Differential Equations", Boulder, CO, July 1999, Contemporary Mathematics, 268 (2000), 117-137.

73. (with J.Cheng, M. Yamamoto, and Q. Zhou) Lipschitz stability in the lateral Cauchy problem for elasticity system, J. Math. Kyoto Univ., 43 (2003), 475-501.

74. (with M.Yamamoto) Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems, Proceedings of the conference "Differential-Geometric Methods in the Control of Partial Differential Equations", Boulder, CO, July 1999, Contemporary Mathematics, 268(2000), 191-227.

75. (with T.DeLillo, N. Valdivia, L. Wang) The detection of the source of acoustical noise in two dimensions, SIAM J. Appl. Math., 61(2001), 2104-2121.

76. Uniqueness of recovery of some quasilinear partial differential equations, Comm. in Part. Diff. Equat., 26 (2001), 1947-1975.

77. Three-dimensional inverse scattering theory and its relation with other problems, A chapter in the book "Scattering", eds. E.R.Pike, P.Sabatier, Academic Press, (2001), 753-769.

78. Carleman estimates and their applications, in "New Analytic and Geometric Methods in Inverse Problems", Springer-Verlag, (2004), 93-127.

79. Uniqueness of recovery of some systems of semilinear equations, Inverse Problems, 17 (2001),607-619.

80. (with I. Bouchouev, N. Valdivia) Recovery of volatility coefficient by linearization, Quant. Finance, 2 (2002), 257-263.

81. (with T. DeLillo, N. Valdivia, L. Wang) The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), 507-524.

82. (with A. Bukhgeim, J. Cheng, M. Yamamoto) Uniqueness in determining damping coefficients in hyperbolic equations, In "Analytic Extensions Formulas and Their Applications", Eds. S. Saitoh, N. Hayashi, M. Yamamoto. Kluwer, 2001, 27-47.

83. (with M. Belishev) On uniqueness of recovery of parameters of the Maxwell system from dynamical boundary data, Zapiski Nauchnych Seminarov POMI, 285 (2001), 1-18.

84. (with S. Wu) On theory and applications of the HELS method in inverse acoustics, Inverse Problems, 18(2002), 1147-1161.

85. (with O. Imanuvilov, M.Yamamoto) An inverse problem for the dynamical Lame system with two sets of boundary data, Comm. Pure Appl. Math., 56 (2003), 1366-1382.

86. Inverse problems for quasilinear equations, In "Nonlinear Problems in Math. Physics and related Topics.II". In honor of prof. O.A. Ladyzhenskaja. Eds. M. Birman, S. Hildebrandt, V. Solonnikov, N. Uraltseva. Kluwer, 2002, 201-212.

87. (with G, Nakamura, J.-N. Wang) On the uniqueness of the continuation for the dynamical Lame system with residual stress, Contemp. Math., AMS, 333(2003), 99-113.

88. (with M. Yamamoto) Stability in a wave source problem by Dirichlet data on subboundary, J. Inverse Ill-Posed Problems, 11(2003), 1-11.

89. (with T. Hrycak) Increased stability in the continuation of solutions to the Helmholtz equation, Inverse Problems, 20(2004), 697-712.

90. Carleman estimates and applications to inverse problems, Milan J. Math., 72(2004), 249-273.

91. An inverse problem for the dynamical Lame system with two sets of local boundary data, "Control Theory for Partial Differential Equations" (Lecture Notes in Pure and Applied Mathematics)., Proc. of the Conference at Georgetown University, May 2003. CRC-Marcel Dekker, 2005, 101-111.

92. (with T. DeLillo, T. Hrycak) Theory and boundary element methods for nearfield acoustic holography, J. Comp. Acoust., 13 (2005), 163-185.

93. (with M. Yamamoto, J.-N. Wang) Uniqueness and stability of determining the residual stress by one measurement,
Comm. Part. Diff. Equat., 32 (2007), 833-848.

94. Increased stability in the continuation for the Helmholtz equation with variable coefficient, Contemporary Math. AMS, 426 (2007), 255-269.

95. Increased stability in the Cauchy problem for some elliptic equations., In ``Instability in Models Connected with Fliud Flow''. Eds. C. Bardos, A. Fursikov, Intern. Math. Series, 6- 7, 2007. Springer-Verlag, 337-360.

96. On uniqueness in the inverse conductivity problem with local data ,
Inverse Problems and Imaging, 1 (2007), 95-105.

97. On uniqueness of obstacles and boundary conditions from the dynamical data Inverse Problems and Imaging , 2 (2008), 151-165.

98.(With M. Yamamoto, J.-N. Wang)   An inverse problems for a dynamical Lame system with resudual stress
SIAM J. Math. Anal. 39, (2007), 1328-1343.

99.(With O. Imanuvilov, M. Yamamoto) New realization of the pseudo convexity and its applications to an inverse problem. Appl. Anal. 88 (2009), 637-653.

100.(With D. Aralumallige Subbarayyappa).  On increased stability of the continuation for the Helmholtz equation., Inverse Problems, 23 (2007), 1689-1697.

101.   The inverse conductivity problem with limited data and applications. Proc. of the conference ``Inverse Problems in Applied Sciences'', Sapporo, Japan, July 2006. IOP Conf. Series, 73 (2007), 012011.

102. On uniqueness of domains and general transmission conditions in inverse scattering. Comm. Math. Phys., 280 (2008), 843-858.

103. On inverse problems in secondary oil recovery. European J. Appl. Math, 19 (2008), 459-478.

104.(with N. Kim)   Carleman estimates with second large parameter and applications to elasticity with residual stress. Applicationes Mathematicae, 35 (2008), 447-465.

105.   On identification of the doping profile in semiconductors. Contemp. Math. AMS, 494 (2009), 123-137.

106.(with N. Kim)   Carleman estimates with second large parameter for second order operators. In ``Some Applications of Sobolev Spaces to PDEs'', Intern. Math. Ser., Vol. 10, Springer-Verlag, 2009, 135-160.

107.   Increasing stability for the Schr\"odinger potential from the Dirichlet-to Neumann map, Discrete and Continuous Dynamical Systems S, 4 (2011), 631-641.

108. (with N. Kim)   Global uniqueness and Lipschitz stability of residual stress from one boundary measurement, ESAIM, Proc. of seminars at IHP, 26 (2009), 45-54.

109.   Inverse Obstacle Problems, Inverse Problems, 25 (2009), 123002.

110. (with N. Kim)   Weak Carleman estimates with two large parameters for seciond order operators and applications to elasticity with residual stress, Discrete and Continuous Dynamical Systems A, 27 (2010), 799-827 .

111. (with D. Aralumallige Subbarayyappa)   Increasing stability of the continuation for the Maxwell system, Inverse Problems,26 (2010), 074005.

112. (with K. Kim, G. Nakamura) Reconstruction of an unknown inclusion by theormography, Annali Scuola Norm. Sup. Pisa, 9 (2010), 725-758.

113. (with S. Leung, J. Qian) A fast Local Level Set Method for Inverse Gravimetry, Comm. Compt. Phys. 10(2011), 1044-1070.

114. ( with S. Kindermann)   Subspaces of stability in the Cauchy problem for the Helmholtz equation, Methods and Applications of Analysis, 18 (2011), 1-30.

115. ( with J. Myers)   On the inverse doping profile problem, Inverse problems and Imaging, 6 (2012), 465-487.

116. Carleman estimates for some anisotropic elasticity systems and applications, Evolution Equations and Control Theory, 1 (2012), 141-154.

117. (with A. Elcrat, E. Kropf, D. Stewart) A stability analysis of the harmonic continuation, Inverse Problems, 28 (2012), 075016.

118. (with S. Leung, J. Qian) A three-dimensional inverse gravimetry problem for ice with snow caps, Inverse Problems and Imaging, 7 (2013), 523-545.

119. (with S. Nagayasu, G. Uhlmann, J.-N. Wang) Increasing stability of the inverse boundary value problem for the Schr\"odinger equation, Contemp. Math., 615 (2014), 131-141.

120. Recovery of time dependent volatility coefficient by linearization, Evolut. Equat. and Control Theory, 3 (2014), 119-134.

121. (with J.-N. Wang) Increasing stability for determining the potential in the Schr\"odinger equation with attenuation from the Dirichlet-to Neumann map, Inverse Problems and Imaging, 8 (2014), 1139-1150.

122. On increasing stability in the Cauchy problem for general elliptic equations, in "New Prospects in Direct, Inverse, and Control Problems", A. Favini et al. (eds), Springer INDAM Series, 10 (2014), 203-218.

123. Increasing stability for near field from the scattering amplitude, Contemp. Math., 640 (2015), 59-70.

124. (with J. Cheng, S. Lu) Increasing stability in the inverse source problem with many frequencies, J. Diff. Equat., 260 (2016), 4786-4804.

125. Locating a source, Encyclopedia of Applied and Computational Mathematics, ed. B. Engquist, Springer-Verlag, 2015, pp. 1340-1344.

126. (with R.-Y. Lai, J. -N. Wang) Increasing stability for the conductivity and attenuation coefficients, SIAM J. Math. Anal., 48 (2016), 569-594.

127. (with Z.-C. Deng, B. Hon) Recovery of time dependent volatility in option pricing model, Inverse Problems, 32 (2016), 115010.

128. Carleman estimates with two large parameters for an anisotropic system of elasticity, Rend. Istit. Matem. dell' Univ. di Trieste, 48 (2016), 261-283.

129. (with S. Lu) Increasing stability in the inverse source problem with attenuation and many frequencies, SIAM J. Appl. Math., (2017, in print).

130. (with S. Lu) Inverse source problem without (pseuso)convexity assumptions, Inverse Probl. Imag., (submitted).

131. (with M. Entekhabi) On increasing stability in the two dimensional inverse source scattering problem with many frequencies, Inverse Probl., (submitted).

Colored titles are available from this site in PDF format.


Books

1. Inverse Source Problems, Math.Surveys and Monographs Series, #34, AMS, Providence, RI, 1990.

2. Inverse Problems in PDE, Appl. Math.Sc., Vol. 127, Springer-Verlag, New York, 1998. Second edition, 2005. Third edition, 2017.

3. Sobolev Spaces in Mathematics, III, Inter. Math.Ser., Vol. 10, Springer, 2009.


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