multidimensional inverrse problems; evolution equations; geometry of convex surfaces; integral geometry; ill-posed problems; tomography.
Subject:
The theory and applications of multidimensional inverse and ill-posed problems were developed.
Biography
Graduated from Novosibirsk state University in 1963. Ph.D. thesis was defended in 1968. D.Sci. thesis was defended in 1978. A list of my works containes more than 170 titles.
The State Prize laureate in 1987 Honoured worker of Russian Federation Academician of Petrovskaya Academy of Sciences and Arts.
Main publications:
Anikonov Yu. E. Multidimensional Inverse and Ill-posed Problems for Differential Equation. VSP, Utrecht, The Netherland, Tokyo, Japan, 1995. 138 p.
Anikonov Yu. E., Bubnov B. A., Erokhin G. N. Inverse and Ill-Posed Sources Problems. VSP, Utrecht, The Netherland, 1997. 239 p.
Anikonov Yu. E. Inverse problems for kinetic and other evolution equations. VSP, Utrecht, The Netherland, 2001. 286 p.
Yu. E. Anikonov, M. V. Neshchadim, A. P. Chupakhin, “Multidimensional Hopf equation and some exact solutions”, Sib. Zh. Ind. Mat., 25:1 (2022), 5–13
2021
2.
Yu. E. Anikonov, V. V. Bogdanov, Yu. S. Volkov, E. Yu. Derevtsov, “On the determination of the velocity and elastic parameters of the focal zone medium from the earthquake hodographs”, Sib. Zh. Ind. Mat., 24:4 (2021), 5–24
Yu. E. Anikonov, N. B. Ayupova, M. V. Neshchadim, “Some representations of solutions to Blokhintsev equation”, Sib. Èlektron. Mat. Izv., 17 (2020), 1697–1709
4.
Yu. E. Anikonov, “Formulas in the theory of identification”, Sib. Èlektron. Mat. Izv., 17 (2020), 1522–1539
5.
Yu. E. Anikonov, “A uniqueness theorem for an inverse kinematic seismic problem”, Sib. Zh. Ind. Mat., 23:1 (2020), 5–10; J. Appl. Industr. Math., 14:1 (2020), 1–5
2019
6.
Yu. E. Anikonov, N. B. Ayupova, M. V. Neshchadim, “Ray expansions and identification questions for Navie–Stockes equations”, Sib. Èlektron. Mat. Izv., 16 (2019), 1567–1580
7.
Yu. E. Anikonov, M. V. Neshchadim, “On a method of studying identification problems for second order equations”, Sib. Zh. Ind. Mat., 22:1 (2019), 13–23; J. Appl. Industr. Math., 13:1 (2019), 11–21
Yu. E. Anikonov, “Operator formulas for differential-difference equations with applications to identification”, Sib. Zh. Ind. Mat., 21:1 (2018), 3–10; J. Appl. Industr. Math., 12:1 (2018), 1–8
11.
Yu. E. Anikonov, “Functional equations and identification problems”, Sib. J. Pure and Appl. Math., 18:2 (2018), 3–12; J. Math. Sci., 246:6 (2020), 727–737
Yu. E. Anikonov, N. B. Ayupova, M. V. Neshchadim, “Ray method and questions of identification of the elasticity theory equations”, Sib. J. Pure and Appl. Math., 18:1 (2018), 11–27; J. Math. Sci., 246:6 (2020), 738–754
N. L. Abasheeva, Yu. E. Anikonov, “Operator formulae in the inverse problems for evolution equations”, Sib. J. Pure and Appl. Math., 17:3 (2017), 8–16; J. Math. Sci., 237:4 (2019), 501–510
14.
Yu. E. Anikonov, N. B. Ayupova, “Ray expansions and identities for the second order equations with applications to inverse problems”, Sib. J. Pure and Appl. Math., 17:1 (2017), 3–16; J. Math. Sci., 231:2 (2018), 111–123
Yu. E. Anikonov, “On some problems of mathematical physics with variable parameter”, Sib. J. Pure and Appl. Math., 16:1 (2016), 3–13; J. Math. Sci., 228:4 (2018), 335–346
2015
16.
Yu. E. Anikonov, M. V. Neshchadim, “The method of differential relations and nonlinear inverse problems”, Sib. Zh. Ind. Mat., 18:2 (2015), 36–47; J. Appl. Industr. Math., 9:3 (2015), 317–327
Yu. E. Anikonov, “Some remarks on functional equations and on their applications”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:4 (2015), 12–23; J. Math. Sci., 221:6 (2017), 745–757
Yu. E. Anikonov, N. B. Ayupova, “On inverse problems in classes of entire functions”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 11–23; J. Math. Sci., 221:6 (2017), 758–771
19.
Yu. E. Anikonov, M. V. Neshchadim, “Algebra-analytical ways of constructing solutions of differential equations and inverse problems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:2 (2015), 3–21; J. Math. Sci., 215:4 (2016), 444–459
Yu. E. Anikonov, N. B. Ayupova, “The Hopf–Cole transformation and multidimensional representations of solutions to evolution equations”, Sib. Zh. Ind. Mat., 17:4 (2014), 31–37; J. Appl. Industr. Math., 9:1 (2015), 11–17
Yu. E. Anikonov, “Representation of solutions to functional and evolution equations and identification problems”, Sib. Èlektron. Mat. Izv., 10 (2013), 591–614
Yu. E. Anikonov, M. V. Neshchadim, “Representations for the solutions and coefficients of evolution equations”, Sib. Zh. Ind. Mat., 16:2 (2013), 40–49; J. Appl. Industr. Math., 7:3 (2013), 326–334
Yu. E. Anikonov, N. B. Aiupova, V. G. Bardakov, V. P. Golubyatnikov, M. V. Neshchadim, “Inversion of mapping and inverse problems”, Sib. Èlektron. Mat. Izv., 9 (2012), 382–432
Yu. E. Anikonov, M. V. Neshchadim, “On inverse problems for equations of mathematical physics with parameter”, Sib. Èlektron. Mat. Izv., 9 (2012), 45–64
Yu. E. Anikonov, M. V. Neshchadim, “Representations for the solutions and coefficients of second-order differential equations”, Sib. Zh. Ind. Mat., 15:4 (2012), 17–23; J. Appl. Industr. Math., 7:1 (2013), 15–21
Yu. E. Anikonov, M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. II”, Sib. Zh. Ind. Mat., 14:2 (2011), 28–33; J. Appl. Industr. Math., 6:1 (2012), 6–11
Yu. E. Anikonov, M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. I”, Sib. Zh. Ind. Mat., 14:1 (2011), 27–39; J. Appl. Industr. Math., 5:4 (2011), 506–518
Yu. E. Anikonov, M. V. Neshchadim, “On Analytical Methods in the Theory of Inverse Problems of Parabolic Equations”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:3 (2011), 20–35; J. Math. Sci., 195:6 (2013), 754–770
Yu. E. Anikonov, Yu. S. Volkov, S. B. Gorshkalev, E. Yu. Derevtsov, S. V. Maltseva, “Certain Criterion for the Horizontal Homogeneity of a Medium in Inverse Kinematic Problem of Seismics”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:3 (2011), 3–19; J. Math. Sci., 195:6 (2013), 741–753
Yu. E. Anikonov, M. V. Neshchadim, “On analytical methods in the theory of inverse problems of mathematical physics”, Sib. Èlektron. Mat. Izv., 7 (2010), 11–61
Yu. E. Anikonov, Yu. V. Krivtsov, M. V. Neshchadim, “Constructive methods in nonlinear control theory problems”, Sib. Zh. Ind. Mat., 13:2 (2010), 30–45
Yu. E. Anikonov, M. V. Neshchadim, “Presentations of Solutions, Coefficients and Symbols of Operator of Evolution Equations and Inverse Problems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 10:2 (2010), 25–36; J. Math. Sci., 186:3 (2012), 352–363
Yu. E. Anikonov, N. L. Abasheieva, N. B. Aiupova, A. I. Kozhanov, M. V. Neshchadim, I. R. Valitov, “Inverse problems for evolution equations”, Sib. Èlektron. Mat. Izv., 5 (2008), 549–580
Yu. E. Anikonov, “Конструктивные методы исследования обратных задач для эволюционных уравнений”, Sib. Zh. Ind. Mat., 11:2 (2008), 3–20; J. Appl. Industr. Math., 3:3 (2009), 301–317
Yu. E. Anikonov, M. V. Neshchadim, “Some Inverse Problems for the Quantum Kinetic Equation”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 8:4 (2008), 13–22
2007
39.
Yu. E. Anikonov, M. V. Neshchadim, “An identity for approximate quantum equations, and inverse problems”, Sib. Zh. Ind. Mat., 10:4 (2007), 3–9; J. Appl. Industr. Math., 3:2 (2009), 149–155
Yu. E. Anikonov, M. Yamamoto, “On one method of investigation of inverse problems”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 7:4 (2007), 3–8
2006
41.
Yu. E. Anikonov, V. V. Bogdanov, E. Yu. Derevtsov, V. L. Miroshnichenko, N. A. Sapozhnikova, “Numerical solution of an inverse kinematic seismic problem with internal sources”, Sib. Zh. Ind. Mat., 9:4 (2006), 3–26
Yu. E. Anikonov, “Analytic representations of solutions of multidimensional inverse
problems for evolution equations”, Dokl. Akad. Nauk, 351:2 (1996), 151–154
43.
Yu. E. Anikonov, M. P. Vishnevskii, “Formulas in an inverse problem for an evolution equation”, Sibirsk. Mat. Zh., 37:5 (1996), 963–976; Siberian Math. J., 37:5 (1996), 847–859
Yu. E. Anikonov, “Relations associated with problems in tomography”, Dokl. Akad. Nauk, 342:2 (1995), 167–168
47.
Yu. E. Anikonov, “Formulas in the inverse problem for the kinetic equation”, Dokl. Akad. Nauk, 340:1 (1995), 5–6
1994
48.
Yu. E. Anikonov, “Formulas in inverse problems for differential equations and
inequalities”, Dokl. Akad. Nauk, 337:1 (1994), 23–24; Dokl. Math., 39:7 (1994), 461–462
49.
Yu. E. Anikonov, “Formulas in a multidimensional inverse problem for an evolution
equation”, Dokl. Akad. Nauk, 334:3 (1994), 263–264; Dokl. Math., 49:1 (1994), 62–63
Yu. E. Anikonov, V. N. Stepanov, “The geometry of convex surfaces and inverse problems of scattering theory”, Sibirsk. Mat. Zh., 35:5 (1994), 955–973; Siberian Math. J., 35:5 (1994), 845–862
Yu. E. Anikonov, M. P. Vishnevskii, “Reduction of multidimensional inverse problems to initial-boundary value problems in Hilbert spaces”, Sibirsk. Mat. Zh., 35:3 (1994), 495–514; Siberian Math. J., 35:3 (1994), 439–458
Yu. E. Anikonov, “An estimate in a problem of integral geometry”, Dokl. Akad. Nauk, 330:4 (1993), 405–406; Dokl. Math., 47:3 (1993), 483–484
1992
54.
Yu. E. Anikonov, O. N. Smirnov, “Some algebraic questions in the theory of multidimensional inverse
problems for nonlinear evolution equations”, Dokl. Akad. Nauk, 324:2 (1992), 303–308; Dokl. Math., 37:5 (1992), 226–228
55.
Yu. E. Anikonov, “Multidimensional inverse problems for evolution equations with
discrete time”, Dokl. Akad. Nauk, 323:6 (1992), 1078–1082; Dokl. Math., 37:4 (1992), 174–176
Yu. E. Anikonov, “Formulas for solutions of some inverse problems for evolution
equations”, Dokl. Akad. Nauk SSSR, 319:5 (1991), 1117–1119; Dokl. Math., 36:8 (1991), 569–570
Yu. E. Anikonov, “Inverse problems in mathematical physics and biology”, Dokl. Akad. Nauk SSSR, 318:6 (1991), 1350–1354; Dokl. Math., 36:6 (1991), 436–438
61.
Yu. E. Anikonov, “Representations of solutions of equations with variable
coefficients, and inverse problems”, Dokl. Akad. Nauk SSSR, 318:5 (1991), 1145–1148; Dokl. Math., 36:6 (1991), 431–433
62.
Yu. E. Anikonov, V. N. Stepanov, “An inversion formula in a problem of integral geometry”, Dokl. Akad. Nauk SSSR, 318:2 (1991), 265–266; Dokl. Math., 43:3 (1991), 678–679
Yu. E. Anikonov, I. Ya. Shneiberg, “The Radon transformation with variable absorption”, Dokl. Akad. Nauk SSSR, 316:1 (1991), 93–95; Dokl. Math., 36:1 (1991), 34–35
1990
64.
Yu. E. Anikonov, “Relations in some inverse problems for nonlinear equations”, Dokl. Akad. Nauk SSSR, 315:4 (1990), 850–853; Dokl. Math., 35:12 (1990), 1027–1028
65.
Yu. E. Anikonov, “Inverse problems for nonlinear equations, and synergetics”, Dokl. Akad. Nauk SSSR, 315:2 (1990), 355–358; Dokl. Math., 35:11 (1990), 930–932
Yu. E. Anikonov, “Some relations in inverse problems for kinetic equations”, Dokl. Akad. Nauk SSSR, 313:2 (1990), 309–312; Dokl. Math., 35:7 (1990), 629–630
67.
Yu. E. Anikonov, “Formulas in multidimensional inverse problems for evolution
equations”, Dokl. Akad. Nauk SSSR, 312:1 (1990), 11–14; Dokl. Math., 41:3 (1990), 385–388
68.
Yu. E. Anikonov, “On the singlevalued solution of inverse problem for quantum kinetic equation”, Mat. Sb., 181:1 (1990), 68–74; Math. USSR-Sb., 69:1 (1991), 69–76
Yu. E. Anikonov, L. N. Pestov, “Integral geometry and the structure of Riemannian spaces”, Dokl. Akad. Nauk SSSR, 307:3 (1989), 521–523; Dokl. Math., 40:1 (1990), 90–93
70.
Yu. E. Anikonov, Yu. Ya. Belov, “Single-valued solvability of an inverse problem for a parabolic
equation”, Dokl. Akad. Nauk SSSR, 306:6 (1989), 1289–1293; Dokl. Math., 39:3 (1989), 601–605
Yu. E. Anikonov, “A linear system of equations of a transport theory that does not
contain cross sections or a scattering indicatrix”, Dokl. Akad. Nauk SSSR, 305:2 (1989), 319–322; Dokl. Math., 34:3 (1989), 210–211
72.
Yu. E. Anikonov, B. A. Bubnov, “Control problems and inverse problems”, Dokl. Akad. Nauk SSSR, 304:2 (1989), 309–312; Dokl. Math., 34:1 (1989), 13–14
Yu. E. Anikonov, B. A. Bubnov, “Inverse problems of transport theory”, Dokl. Akad. Nauk SSSR, 299:5 (1988), 1037–1040; Dokl. Math., 37:2 (1988), 497–500
Yu. E. Anikonov, B. A. Bubnov, “Existence and uniqueness of the solution of an inverse problem for
a parabolic equation”, Dokl. Akad. Nauk SSSR, 298:4 (1988), 777–779; Dokl. Math., 37:1 (1988), 130–132
Yu. E. Anikonov, A. N. Bondarenko, “Multidimensional inverse problems for kinetic equations”, Dokl. Akad. Nauk SSSR, 277:4 (1984), 779–781
76.
Yu. E. Anikonov, “A criterion for two-dimensional Riemann spaces of zero curvature”, Mat. Zametki, 35:6 (1984), 841–845; Math. Notes, 35:6 (1984), 441–443
1983
77.
Yu. E. Anikonov, A. Kh. Amirov, “A uniqueness theorem for the solution of an inverse problem for a kinetic equation”, Dokl. Akad. Nauk SSSR, 272:6 (1983), 1292–1293
Yu. E. Anikonov, “Solutions of a class of converse problems”, Mat. Zametki, 33:2 (1983), 247–250; Math. Notes, 33:2 (1983), 125–126
1982
79.
Yu. E. Anikonov, A. N. Bondarenko, “The inverse problem for the Vlasov equation”, Dokl. Akad. Nauk SSSR, 265:5 (1982), 1037–1039
1981
80.
Yu. E. Anikonov, V. N. Stepanov, “Uniqueness and stability of the solution of a problem of geometry in the large”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 539–546; Math. USSR-Sb., 44:4 (1983), 483–490
Yu. E. Anikonov, V. N. Moskvitin, “On an inverse problem for the system of dynamical equations of elasticity theory”, Dokl. Akad. Nauk SSSR, 253:5 (1980), 1086–1087
Yu. E. Anikonov, “Uniqueness of the solution of integral equations of the first kind with entire kernels”, Mat. Zametki, 28:3 (1980), 401–405; Math. Notes, 28:3 (1980), 669–671
Yu. E. Anikonov, “Uniqueness of the solution of the inverse problems in classes of entire functions”, Funktsional. Anal. i Prilozhen., 13:4 (1979), 57–58; Funct. Anal. Appl., 13:4 (1979), 282–283
1976
86.
Yu. E. Anikonov, “A uniqueness theorem for the solution of the inverse problem for a quasilinear hyperbolic equation”, Differ. Uravn., 12:12 (1976), 2265–2266
87.
Yu. E. Anikonov, “A uniqueness theorem for solutions to an inverse problem for the wave equation”, Mat. Zametki, 19:2 (1976), 211–214; Math. Notes, 19:2 (1976), 127–128
Yu. E. Anikonov, “On the solvability of a problem in integral geometry”, Mat. Sb. (N.S.), 101(143):2(10) (1976), 271–279; Math. USSR-Sb., 30:2 (1976), 239–247
Yu. E. Anikonov, “On the problem of determining the Riemannian metric $ds^2=\lambda^2(x)|dx|^2$”, Mat. Zametki, 16:4 (1974), 611–617; Math. Notes, 16:4 (1974), 956–960
1973
90.
Yu. E. Anikonov, “The uniqueness of the solution of integral equations of the first kind”, Mat. Zametki, 14:4 (1973), 493–498; Math. Notes, 14:4 (1973), 840–843
91.
Yu. E. Anikonov, “Determination of the metric of a Liouville surface”, Sibirsk. Mat. Zh., 14:6 (1973), 1338–1340; Siberian Math. J., 14:6 (1973), 943–945
1972
92.
Yu. E. Anikonov, “On operator equations of the first kind”, Dokl. Akad. Nauk SSSR, 207:2 (1972), 257–258
93.
Yu. E. Anikonov, “On a problem of defining a Riemannian metric”, Dokl. Akad. Nauk SSSR, 204:6 (1972), 1287–1288
Yu. E. Anikonov, “Unique determination of a convex surface and of a function defined on it”, Mat. Zametki, 12:4 (1972), 421–424; Math. Notes, 12:4 (1972), 685–687
95.
Yu. E. Anikonov, “An inverse problem for an ordinary second-order differential equation”, Mat. Zametki, 12:2 (1972), 163–166; Math. Notes, 12:2 (1972), 533–535
Yu. E. Anikonov, “A certain class of operator equations”, Sibirsk. Mat. Zh., 13:6 (1972), 1383–1386; Siberian Math. J., 13:6 (1972), 974–976
1971
97.
M. M. Lavrent'ev, Yu. E. Anikonov, F. N. Fazylov, “Approximate solution of some nonlinear operator equations”, Dokl. Akad. Nauk SSSR, 200:4 (1971), 770–772
98.
Yu. E. Anikonov, “Level surfaces of a function defining a Riemann metric”, Mat. Zametki, 9:6 (1971), 709–711; Math. Notes, 9:6 (1971), 410–411
99.
Yu. E. Anikonov, “Uniqueness theorems for certain problems of variational calculus”, Sibirsk. Mat. Zh., 12:1 (1971), 212–215; Siberian Math. J., 12:1 (1971), 154–156
1970
100.
Yu. E. Anikonov, “A uniqueness theorem for a certain variational problem”, Sibirsk. Mat. Zh., 11:2 (1970), 461–463; Siberian Math. J., 11:2 (1970), 351–353
1969
101.
Yu. E. Anikonov, “Uniqueness theorem for convex surfaces”, Mat. Zametki, 6:1 (1969), 115–117; Math. Notes, 6:1 (1969), 528–529
1968
102.
Yu. E. Anikonov, “Remarks on convex surfaces”, Sibirsk. Mat. Zh., 9:6 (1968), 1413–1415; Siberian Math. J., 9:6 (1968), 1058–1059
Yu. E. Anikonov, S. I. Kabanikhin, V. G. Romanov, “Mikhail Mikhaĭlovich Lavrent'ev”, Sib. Zh. Ind. Mat., 13:3 (2010), 3–5
2002
105.
Yu. E. Anikonov, A. L. Bukhgeim, V. P. Golubyatnikov, S. I. Kabanikhin, V. G. Romanov, “Mikhail Mikhailovich Lavrent'ev (on the occasion of his seventieth birthday)”, Sib. Zh. Ind. Mat., 5:2 (2002), 3–6
1992
106.
Yu. E. Anikonov, N. N. Bogolyubov, Yu. L. Ershov, A. B. Zhizhchenko, E. F. Mishchenko, V. G. Romanov, “Mikhail Mikhailovich Lavrent'ev (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 47:3(285) (1992), 183–185; Russian Math. Surveys, 47:3 (1992), 197–200
1982
107.
A. S. Alekseev, Yu. E. Anikonov, V. G. Romanov, “On the occasion of the fiftieth birthday of Academician M. M. Lavrent'ev”, Sibirsk. Mat. Zh., 23:5 (1982), 3–4