Vladimir Gavrilovich Romanov — leader of the Siberian School of Inverse Problems

S. I. Kabanikhin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. A1-A20

Résumé

On the occasion of 85th birthday of Vladimir Gavrilovich Romanov, we give a brief description of his works, achievements and biography.

Détail

Keywords: inverse problems, biography.

Bibliographie

[1] V.G. Romanov, “An inverse problem for a nonlinear transport equation”, Sib. Math. J., 65:5 (2024), 1195–1200 | DOI | MR | Zbl

[2] M.V. Klibanov, V.G. Romanov, “A Hölder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave”, J. Inverse Ill-Posed Probl., 31:2 (2023), 223–242 | MR | Zbl

[3] V.G. Romanov, “An inverse problem for electrodynamic equations with nonlinear conductivity”, Dokl. Math., 107:1 (2023), 53–56 | DOI | MR | Zbl

[4] A. Hasanov, V. Romanov, O. Baysal, “Unique recovery of unknown spatial load in damped Euler-Bernoulli beam equation from final time measured output”, Inverse Probl., 37:7 (2021), 075005 | DOI | MR | Zbl

[5] V.G. Romanov, M. Yamamoto, “Recovering two coefficients in an elliptic equation via phaseless information”, Inverse Probl. Imaging, 13:1 (2019), 81–91 | DOI | MR | Zbl

[6] V.G. Romanov, “Phaseless inverse problems that use wave interference”, Sib. Math. J., 59:3 (2018), 494–504 | DOI | MR | Zbl

[7] V.G. Romanov, “Regularization of a solution to the Cauchy problem with data on a timelike plane”, Sib. Math. J., 59:4 (2018), 694–704 | DOI | MR | Zbl

[8] V.G. Romanov, “Estimation of the solution stability of the Cauchy problem with the data on a time-like plane”, J. Appl. Ind. Math., 12:3 (2018), 531–539 | DOI | MR | Zbl

[9] V.G. Romanov, M. Yamamoto, “Phaseless inverse problems with interference waves”, J. Inverse Ill-Posed Probl., 26:5 (2018), 681–688 | DOI | MR | Zbl

[10] M.V. Klibanov, V.G Romanov, “Uniqueness of a 3-D coefficient inverse scattering problem without the phase information”, Inverse Probl., 33:9 (2017), 095007 | DOI | MR | Zbl

[11] V.G Romanov, M. Yamamoto, “Phaseless inverse problems with interference waves”, J. Inverse Ill-Posed Probl., 26:5 (2018), 681–688 | DOI | MR | Zbl

[12] V.G Romanov, “The problem of recovering the permittivity coefficient from the modulus of the scattered electromagnetic field”, Sib. Math. J., 58:4 (2017), 711–717 | DOI | MR | Zbl

[13] M.V. Klibanov, V.G. Romanov, “Uniqueness of a 3-D coefficient inverse scattering problem without the phase information”, Inverse Probl., 33:9 (2017), 095007 | DOI | MR | Zbl

[14] A. Hasanov Hasanoğlu, V.G. Romanov, Introduction to inverse problems for differential equations, Springer, Cham, 2017 | MR | Zbl

[15] M.V. Klibanov, V.G. Romanov, “Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation”, Inverse Probl., 32:2 (2016), 015005 | DOI | MR | Zbl

[16] M.V. Klibanov, V.G. Romanov, “Reconstruction procedures for two inverse scattering problem without the phase information”, SIAM J. Appl. Math., 76:1 (2016), 178–196 | DOI | MR | Zbl

[17] M.V. Klibanov, V.G. Romanov, “Explicit formula for the solution of the phaseless inverse scattering problem of imaging of nano structures”, J. Inverse Ill-Posed Probl., 23:2 (2015), 187–193 | DOI | MR | Zbl

[18] M.V. Klibanov, V.G. Romanov, “Explicit solution of 3-D phaseless inverse scattering problems for the Schrödinger equation: the plane wave case”, Eurasian J. Math. Comput. Appl., 3:1 (2015), 48–63 | MR

[19] V.G. Romanov, “An asymptotic expansion of the fundamental solution for a parabolic equation and inverse problems”, Dokl. Math., 92:2 (2015), 541–544 | DOI | MR | Zbl

[20] M.V. Klibanov, V.G. Romanov, “The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation”, J. Inverse Ill-Posed Probl., 23:4 (2015), 415–428 | DOI | MR | Zbl

[21] V.G. Romanov, “Some geometric aspects in inverse problems”, Eurasian J. Math. Comput. Appl., 3:4 (2015), 68–84

[22] V.G. Romanov, “On the determination of the coefficients in the viscoelasticity equations”, Sib. Math. J., 55:3 (2014), 503–510 | DOI | MR | Zbl

[23] V.G. Romanov, “Recovering jumps in X-ray tomography”, J. Appl. Ind. Math., 8:4 (2014), 582–593 | DOI | MR | Zbl

[24] V.G. Romanov, “Inverse problems for differential equations with memory”, Eurasian J. Math. Comput. Appl., 2:4 (2014), 51–80 | MR

[25] A. Hasanov, V.G. Romanov, “An inversion coefficient problem related to elastic-plastic torsion of a circular cross-section bar”, Appl. Math. Lett., 26:5 (2013), 533–538 | DOI | MR | Zbl

[26] V.G. Romanov, “An asymptotic expansion for a solution to viscoelasticity equations”, Eurasian J. Math. Comput. Appl., 1:1 (2013), 41–61

[27] V.G. Romanov, “A two-dimensional inverse problem for the viscoelasticity equation”, Sib. Math. J., 53:6 (2012), 1128–1138 | DOI | MR | Zbl

[28] V.G. Romanov, “A three-dimensional inverse problem of viscoelasticity”, Dokl. Math., 84:3 (2011), 833–836 | DOI | MR | Zbl

[29] V.G. Romanov, “A two-dimensional inverse problem of viscoelasticity”, Dokl. Math., 84:2 (2011), 649–652 | DOI | MR | Zbl

[30] V.G. Romanov, “Stability estimate of a solution to the problem of kernel determination in integrodifferential equations of electrodynamics”, Dokl. Math., 84:1 (2011), 518–521 | DOI | MR | Zbl

[31] A. Lorenzi, V.G. Romanov, “Recovering two Lamé kernels in a viscoelastic system”, Inverse Probl. Imaging, 5:2 (2011), 431–464 | DOI | MR | Zbl

[32] V.G. Romanov, “The inverse diffraction problem for acoustic equations”, Dokl. Math., 81:2 (2010), 238–240 | DOI | MR | Zbl

[33] V.G. Romanov, M. Yamamoto, “Recovering a Lamé kernel in a viscoelastic equation by a single boundary measurement”, Appl. Anal., 89:3 (2010), 377–390 | DOI | MR | Zbl

[34] V.G. Romanov, S.I. Kabanikhin, M.A. Shishlenin, “Investigation of the mathematical model of an electromagnetic probe in an axisymmetric well”, Proceedings of the first international scientific school-conference for young scientists «Theory and numerical methods for solving inverse and ill-posed problem», Sib. Èlektron. Mat. Izv., 7, eds. S.I. Kabanikhin, M.A. Shishlenin, 2010, 307–321 | MR

[35] V.G. Romanov, “A stability estimate for the solution to the Ill-posed Cauchy problem for elasticity equations”, J. Inverse Ill-Posed Probl., 16:6 (2008), 615–623 | DOI | MR | Zbl

[36] V.G. Romanov, “Estimate of the solution to the Cauchy problem for an ultrahyperbolic inequality”, Dokl. Math., 74:2 (2006), 751–754 | DOI | MR | Zbl

[37] V.G. Romanov, “Stability estimate for the solution to the elasticity equations with data on a timelike surface”, Dokl. Math., 74:2 (2006), 653–655 | DOI | MR | Zbl

[38] V.G. Romanov, “Stability estimate in the problem of extending the solution to the wave equation from a timelike cylindrical surface”, Dokl. Math., 72:2 (2005), 690–693 | MR | Zbl

[39] V.G. Romanov, “An example of the absence of a global solution to some inverse problem for a hyperbolic equation”, Sib. Math. J., 44:5 (2003), 867–868 | DOI | MR | Zbl

[40] V.G. Romanov, “Uniqueness theorems for an inverse problem related to local heterogeneities and data on a piece of a plane”, Ill-posed and inverse problems, eds. Romanov V.G. et al., VSP, Utrecht, 2002, 383–398 | DOI | MR | Zbl

[41] S. He, V.G. Romanov, H. Zhang, “Explicit identification of a small breast cancer in a mammography”, J. Inverse Ill-Posed Probl., 10:1 (2002), 23–36 | DOI | MR | Zbl

[42] S. He, V.G. Romanov, “An optical tomography-related time-domain inverse problem for the diffusion equation”, J. Inverse Ill-Posed Probl., 7:4 (1999), 365–380 | DOI | MR | Zbl

[43] V.G. Romanov, “Stability estimate in the inverse problem of determining the speed of sound”, Sib. Math. J., 40:6 (1999), 1119–1133 | DOI | MR | Zbl

[44] V.G. Romanov, S.I. Kabanikhin, “Direct and inverse problems of electromagnetoelasticity”, Physics and Chemistry of the Earth, 23:9-10 (1998), 883–894 | DOI | MR

[45] A.S. Alekseev, S.V. Goldin, V.G. Romanov, “Geotomography: theory, numerical methods, creation of effective algorithms, stability assessment”, Integration Program of Fundamental Research, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 1998, 8–24

[46] V.G. Romanov, J. Gottlieb, S.I. Kabanikhin, S.V. Martakov, “An inverse problem for special dispersive media arising from ground penetrating radar”, J. Inverse Ill-Posed Probl., 5:2 (1997), 175–192 | DOI | MR | Zbl

[47] V.G. Romanov, J. Gottlieb, S.I. Kabanikhin, S. Schlaeger, “Identification of electromagnetic parameters for media with microstructure”, Conference on Inverse Problems of Wave Propagation and Diffraction (Aix-les-Bains, France, September 23-27, 1996), 1996, 18–21

[48] V.G. Romanov, “A stability estimate in the problem of determining the dispersion index and relaxation for the transport equation”, Sib. Math. J., 37:2 (1996), 308–324 | DOI | MR | Zbl

[49] S. He, V.G. Romanov, “An analysis of the time-domain electromagnetic inverse problem of determining the susceptibility kernel for a stratified dispersive slab”, J. Inverse Ill-Posed Probl., 3:6 (1996), 469–494 | MR | Zbl

[50] V.G. Romanov, “On an inverse problem for a coupled system of equations of electrodynamics and elasticity”, J. Inverse Ill-Posed Probl., 3:4 (1995), 321–332 | DOI | MR | Zbl

[51] V.G. Romanov, S. He, S.I. Kabanikhin, S. Ström, “Analysis of the Green's function approach to one-dimensional inverse problems. I. One parameter reconstruction”, J. Math. Phys., 34:12 (1993), 5724–5746 | DOI | MR | Zbl

[52] V.G. Romanov, S.I. Kabanikhin, Inverse problems for Maxwell's equations, VSP, Utrecht, 1994 | MR | Zbl

[53] V.G. Romanov, “Stability estimates for inverse problems of geoelectrics”, Ill-posed problems in natural sciences, Proceedings of the international conference (Moscow, Russia, August 19-25, 1991), eds. Tikhonov A. N. et al., VSP, Utrecht, 1992, 408–416 | DOI | MR | Zbl

[54] A. Alekseev, M.M. Lavrent'ev, V.G. Romanov, M.E. Romanov, “Theoretical and computational aspects of seismic tomography”, Serveys in Geophysics, 11 (1990), 395–409 | DOI

[55] V.G. Romanov, S.I. Kabanikhin, G.B. Bakanov, “Investigation of a differential-difference analogue of a three-dimensional problem in integral geometry”, Sov. Math., Dokl., 41:2 (1990), 306–309 | MR | Zbl

[56] V.G. Romanov, “On the solvability of inverse problems for hyperbolic equations in a class of functions analytic in some of the variables”, Sov. Math., Dokl., 39:1 (1989), 160–164 | MR | Zbl

[57] V.G. Romanov, “Local solvability of some multidimensional inverse problems for hyperbolic equations”, Differ. Equations, 25:2 (1989), 203–209 | MR | Zbl

[58] M.M. Lavrent'ev, V.G. Romanov, S.P. Shishatskii, Ill-posed problems of mathematical physics and analysis, Translations of Mathematical Monographs, 64, AMS, Providence, 1986 | DOI | MR | Zbl

[59] V.G. Romanov, S.I. Kabanikhin, K. Boboev, “An inverse problem for $P_n$-approximation of the kinetic transport equation”, Sov. Math., Dokl., 29 (1984), 496–499 | MR | Zbl

[60] V.G. Romanov, S.I. Kabanikhin, K.S. Abdiev, Numerical methods for solving one-dimensional inverse problems of electrodynamics, Preprint No542, Computing Center of the SB Academy of Sciences of the USSR, Novosibirsk, 1984 | MR

[61] V.G. Romanov, S.I. Kabanikhin, T.P. Pukhnacheva, “On the theory of inverse problems of electrodynamics”, Sov. Math., Dokl., 26:2 (1982), 476–479 | MR | Zbl

[62] V.G. Romanov, Inverse problems for differential equations. Inverse kinematic problem of seismology, Novosibirsk State University, Novosibirsk, 1978 | MR | Zbl

[63] R.G. Mukhometov, V.G. Romanov, “On the problem of determining an isotropic Riemannian metric in n-dimensional space”, Sov. Math., Dokl., 19 (1978), 1330–1333 | MR | Zbl

[64] V.G. Romanov, “Integral geometry on geodesics of an isotropic Riemannian metric”, Sov. Math., Dokl., 19:4 (1978), 847–851 | MR | Zbl

[65] V.G. Romanov, “Unique-solution classes for Volterra operator equations of the first kind”, Funct. Anal. Appl., 9:1 (1975), 78–79 | DOI | MR | Zbl

[66] V.G. Romanov, “On some classes of uniqueness for the solution of integral geometry problems”, Math. Notes, 16:4 (1974), 983–989 | DOI | MR | Zbl

[67] V.G. Romanov, “On the uniqueness of the definition of an isotropic Riemannian metric inside a domain in terms of the distances between points of the boundary”, Sov. Math., Dokl., 15:5 (1974), 1341–1344 | MR | Zbl

[68] V.G. Romanov, Integral geometry and inverse problems for hyperbolic equations, Springer Tracts in Natural Philosophy, 26, Springer Verlag, Berlin etc., 1974 | DOI | Zbl

[69] M.M. Lavrentev, V.G. Romanov, V.G. Vasilev, Multidimensional inverse problems for differential equations, Lecture Notes in Mathematics, 167, Springer Verlag, Berlin etc., 1970 | DOI | MR | Zbl

[70] V.G. Romanov, Inverse problems for differential equations, Novosibirsk State University, Novosibirsk, 1973 | MR | Zbl

[71] A.S. Alekseev, A.V. Belonosova, V.G. Romanov et al., “Seismic studies of low-velocity layers and horizontal inhomogeneities within the crust and upper mantle on the territory of the USSR”, Tectonophysics, 20 (1973), 47–56 | DOI

[72] V.G. Romanov, “A uniqueness and stability theorem for a nonlinear operator equation”, Sov. Math., Dokl., 13 (1972), 1673–1675 | MR | Zbl

[73] V.G. Romanov, “Uniqueness theorems for a certain class of inverse problems”, Sov. Phys., Dokl., 17:6 (1972), 525–526 | MR | Zbl

[74] A.S. Alekseev, M.M. Lavrentiev, V.G. Romanov, R.G. Mukhametov, “A numerical method for determining the structure of the Earth's upper mantle”, Mathematical Problems of Geophysics, v. 2, Computing Center of the SB Academy of Sciences of the USSR, Novosibirsk, 1971, 143–165 | MR

[75] V.G. Romanov, “A certain integral geometry problem, and a linearized inverse problem for a hyperbolic equation”, Sib. Math. J., 10:6 (1969), 1011–1018 | DOI | MR | Zbl

[76] V.G. Romanov, “A formulation of the inverse problem for the generalized wave equation”, Sov. Math., Dokl., 9 (1968), 891–894 | MR | Zbl

[77] V.G. Romanov, “A one-dimensional inverse problem for the telegraph equation”, Differ. Equations, 4:1 (1968), 87–101 | MR | Zbl

[78] V.G. Romanov, “Reconstructing a function by means of integrals along a family of curves”, Sov. Math., Dokl., 8:5 (1967), 923–925 | MR

[79] V.G. Romanov, “Reconstructing a function by means of integrals along a family of curves”, Sib. Mat. Zh., 8 (1967), 1206–1208 | MR | Zbl

[80] M.M. Lavrentiev, V.G. Romanov, “Three linearized inverse problems for hyperbolic equations”, Sov. Math., Dokl., 7:6 (1966), 1650–1652 | MR | Zbl

[81] V.G. Romanov, Investigation methods for inverse problems, VSP, Utrecht, 2002 | MR | Zbl

[82] V.G. Romanov, Stability in inverse problems, Nauchnyĭ Mir, M., 2005 | MR | Zbl

[83] V.G. Romanov, Inverse problems of mathematical physics, Nauka, M., 1984 | MR | Zbl

[84] V.G. Romanov, “Stability estimates for the solution in the problem of determining the kernel of the viscoelasticity equation”, J. Appl. Ind. Math., 6:3 (2012), 360–370 | DOI | MR | Zbl

[85] V.G. Romanov, Certain inverse problems for equations of hyperbolic type, Nauka, Novosibirsk, 1972 | MR | Zbl

[86] V.G. Romanov, S.I. Kabanikhin, Inverse problems of geoelectrics, Nauka, M., 1991 | MR

[87] A. Hasanov Hasanoğlu, V.G. Romanov, Introduction to inverse problems for differential equations, Springer, Cham, 2021 | MR | Zbl

[88] V.G. Romanov, S.I. Kabanikhin, Inverse problems for Maxwell's equations, VSP, Utrecht, 1994 | MR | Zbl