Scientific interests are in the field of the theory of boundary-value problems for the Korteweg–de Vries equation and its generalizations. Results on nonlocal resolvability and well-posedness of initial and initial boundary-value problems in different domains are established for the Korteweg–de Vries equation and its generalizations, including the cases of several space variables and high odd order equations. For initial boundary-value problems construction and investigation of special solutions of boundary potential type to corresponding linear equations are the essential part of the study.
Biography
Graduated from Faculty of Mechanics and Mathematics of Lomonosov Moscow State University in 1980 (Department of Differential Equations). Ph.D thesis was defended in 1984. Dr.Sc thesis was defended in 2001.
Main publications:
Andrei V. Faminskii, “Initial-boundary value problems in a half-strip for two-dimensional Zakharov-Kuznetsov equation”, Annales de lInstitut Henri Poincare C, Analyse Non Lineaire, 35:5 (2018), 1235–1265
Andrei V. Faminskii, “Initial-boundary value problems in a rectangle for two -dimensional Zakharov-Kuznetsov equation”, Journal of Mathematical Analysis and Applications, 463 (2018), 760-793
Andrei V. Faminskii, “An initial–boundary value problem for three-dimensional Zakharov–Kuznetsov equation”, Journal of Differential Equations, 260 (2016), 3029–3055
Andrei V. Faminskii, “An initial-boundary value problem in a strip for two-dimensional Zakharov–Kuznetsov–Burgers equation”, Nonlinear Analysis, 116 (2015), 132–144
Andrei V. Faminskii, “An initial-boundary value problem in a strip for two-dimensional equations of Zakharov–Kuznetsov type”, Contemporary Mathematics, 653, American Mathmatical Society, 2015, 137–162
Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Andrei Faminskii, Fábio Natali, “Decay of solutions to damped Korteweg–de Vries type equation”, Apllied Mathematics & Optimization, 65:2 (2012), 221–251
Andrei V. Faminskii, “Weak solutions to initial-boundary-value problems for quasilinear equations of an odd order”, Advances in Differential Equations, 17:5–6 (2012), 421–470
Andrei V. Faminskii, “Well-posed initial-boundary value problems for the Zakharov–Kuznetsov equation”, Electronic Journal of Differential Equations, 2008:127 (2008), 1–23
A. V. Faminskii, “Global well-posedness of two initial–boundary-value problems for the Korteweg–de Vries equation”, Differential Integral Equations, 20:6 (2007), 601–642
A. V. Faminskii, “An initial boundary-value problem in a half-strip for the Korteweg–de Vries equation in fractional-order Sobolev spaces”, Comm. Partial Differential Equations, 29:11–12 (2004), 1653–1695
A. V. Faminskii, “Mixed problems for the Korteweg–de Vries equation”, Sb. Math., 190:6 (1999), 903–935
A. V. Faminskii, “The Cauchy problem for the Zakharov–Kuznetsov equation”, Differential Equations, 31:6 (1995), 1002–1012
A. V. Faminskii, “Cauchy problem for the generalized Kadomtsev–Petviashvili equation”, Siberian Math. Journal, 33:1 (1992), 133–143
A. V. Faminskii, “The Cauchy problem for odd-order quasilinear equations”, Math. USSR-Sb., 68:1 (1991), 31–59
S. N. Kruzhkov, A. V. Faminskii, “Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation”, Math. USSR-Sb., 48:2 (1984), 391–421
O. S. Balashov, A. V. Faminskii, “Inverse initial-boundary value problem for systems of quasilinear evolution equations of odd order”, Nonlocal and nonlinear problems, CMFD, 71, no. 1, PFUR, M., 2025, 18–32
2.
A. V. Faminskii, “Initial-boundary value problems for the three-dimensional Zakharov-Kuznetsov equation”, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Zap. Nauchn. Sem. POMI, 536, POMI, St. Petersburg, 2024, 336–378
3.
O. S. Balashov, A. V. Faminskii, “On direct and inverse problems for systems of odd-order quasilinear evolution equations”, Eurasian Math. J., 15:4 (2024), 33–53
Andrei V. Faminskii, “Global weak solutions of an initial-boundary value problem on a half-line for the higher order nonlinear Schrödinger equation”, Journal of Mathematical Analysis and Applications, 533 (2024), 128003 , 22 pp.
Andrei V. Faminskii, “On boundary controllability for the higher-order nonlinear Schrödinger equation”, Axioms, 12 (2023), 1127 , 15 pp.
6.
Andrei V. Faminskii, “On inverse problems for odd-order quasilinear evolution equations with general nonlinearity”, Journal of Mathematical Sciences, 271:3 (2023), 281–299
A. V. Faminskii, E. V. Martynov, “Inverse problems for the higher order nonlinear Schrodinger equation”, Journal of Mathematical Sciences, 274:4 (2023), 475–492
Andrei V. Faminskii, “The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis”, Advances in Differential Equations, 28:5–6 (2023), 413–466
9.
Andrei V. Faminskii, “Initial-boundary value problems on a half-strip for the generalized Kawahara-Zakharov-Kuznetsov equation”, Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 73:3 (2022), 93 , 27 pp.
Andrei V. Faminskii, “Initial-boundary value problems on a half-strip for the modified Zakharov–Kuznetsov equation”, Journal of Evolution Equations, 21:2 (2021), 1263–1298
A. V. Faminskii, “Odd-order quasilnear evolution equations with general nonlinearity on bounded domains”, Lobachevskii Journal of Mathematics, 42:5 (2021), 875–888
Marcelo M. Cavalcanti, Wellington J. Corrêa, Andrei V. Faminskii, Mauricio A. Sepulveda C., Rodrigo Vejar-Asem, “Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized damping”, Computers and Mathematics with Applications, 96 (2021), 188–208
A. V. Faminskii, E. V. Martynov, “Large-time decay of solutions of the damped Kawahara equation on the half-line”, Differential Equations on Manifolds and Mathematical Physics, Trends in Mathematics, Research Perspectives, eds. V. M. Manuilov et al, Birkhäuser, 2021, 130–141
14.
Andrei V. Faminskii, “Regular solutions to initial-boundary value problems in a half-strip for two-dimensional Zakharov–Kuznetsov equation”, Nonlinear Analysis: Real World Applications, 51 (2020), 102959 , 21 pp.
Andrei V. Faminskii, “Control problems with an integral condition for Korteweg–de Vries equation on unbounded domains”, Journal of Optimization Theory and Applications, 180:1 (2019), 290–302
A. V. Faminskii, “On inner regularity of solutions of two-dimensional Zakharov-Kuznetsov equation”, Journal of Mathematical Sciences, 265:2 (2022), 313–344
17.
A. V. Faminskii, “Controllability problems for the Korteweg–de Vries equation with integral overdetermination”, Differential Equations, 55:1 (2019), 1–12
18.
A. V. Faminskii, E. V. Martynov, “On initial-boundary value problem on semiaxis for generalized Kawahara equation”, Journal of Mathematical Sciences, 265:5 (2022), 849–864
19.
Andrei V. Faminskii, “On one control problem for Zakharov–Kuznetsov equation”, Analysis, Probability, Applications, and Computation, Trends in Mathematics, Research Perspectives, eds. Karl-Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Walhberg, Birkhäuser, 2019, 305–313
20.
Andrei V. Faminskii, “Initial-boundary value problems in a half-strip for two-dimensional Zakharov-Kuznetsov equation”, Annales de lInstitut Henri Poincare C, Analyse Non Lineaire, 35:5 (2018), 1235–1265
Andrei V. Faminskii, “Initial-boundary value problems in a rectangle for two -dimensional Zakharov-Kuznetsov equation”, Journal of Mathematical Analysis and Applications, 463 (2018), 760-793
Andrei V. Faminskii, “On Strichartz estimates in an abstract form”, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, Research Perspectives, eds. Pei Dang, Min Ku, Tao Qian, Luigi G. Rodino, Birkhäuser, 2017, 473–480
23.
Andrei V. Faminskii, “An initial–boundary value problem for three-dimensional Zakharov–Kuznetsov equation”, Journal of Differential Equations, 260 (2016), 3029–3055
M. A. Opritova, A. V. Faminskii, “On the Cauchy problem for the generalized Kawahara equation”, Differential Equations, 52:3 (2016), 373–385
25.
A. V. Faminskii, A. A. Nikolaev, “On stationary solutions of KdV and mKdV equations”, Differential and Difference Equations with Applications, Springer Proceedings in Mathematics & Statistics, 164, eds. S. Pinelas et al., Springer International Publishing Switzerland, 2016, 63–70
A. P. Antonova, A. V. Faminskii, “On the Regularity of Solutions of the Cauchy Problem for the Zakharov–Kuznetsov Equation in Hölder Norms”, Math. Notes, 97:1 (2015), 12–20
27.
Andrei V. Faminskii, “An initial-boundary value problem in a strip for two-dimensional Zakharov–Kuznetsov–Burgers equation”, Nonlinear Analysis, 116 (2015), 132–144
A. P. Antonova, A. V. Faminskii, “On internal regularity of solutions to the initial value problem for the Zakharov–Kuznetsov equation”, Bulletin of Tambov University, 20:5 (2015), 999–1006
29.
M. A. Opritova, A. V. Faminskii, “On large-time decay of solutions to an initial-boundary value problem on a semi-axis for the generalized Kawahara equation”, Bulletin of Tambov University, 20:5 (2015), 1331–1337
30.
Andrei V. Faminskii, “An initial-boundary value problem in a strip for two-dimensional equations of Zakharov–Kuznetsov type”, Contemporary Mathematics, 653, American Mathmatical Society, 2015, 137–162
A. P. Antonova, A. V. Faminskii, “On regularity of solutions for initial-boundary value problems for the Zakharov–Kuznetsov equation”, Journal of Mathematical Sciences, 233:4 (2018), 427–445
32.
Andrei V. Faminskii, Mariya A. Opritova, “On the initial-boundary-value problem in a half-strip for a generalized Kawahara equation”, Journal of Mathematical Sciences, 206:1 (2015), 17–38
33.
A. V. Faminskii, A. P. Antonova, “On internal regularity of solutions to the initial value problem for the Zakharov–Kuznetsov equation”, Progress in Partial Differential Equations, Asymptotic Profiles, Regularity and Well-Posedness, Springer Proceedings in Mathematics & Statistics, 44, eds. M. Reissig, M. Ruzhansky, Springer International Publishing, 2013, 53–74
Evgeniya S. Baykova, Andrei V. Faminskii, “On initial-boundary value problems in a strip for generalized two-dimensional Zakharov–Kuznetsov equation”, Advances in Differential Equations, 18:7–8 (2013), 663–686
35.
Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, Andrei Faminskii, Fábio Natali, “Decay of solutions to damped Korteweg–de Vries type equation”, Apllied Mathematics & Optimization, 65:2 (2012), 221–251
Andrei V. Faminskii, “Weak solutions to initial-boundary-value problems for quasilinear equations of an odd order”, Advances in Differential Equations, 17:5–6 (2012), 421–470
37.
A.V. Faminskii, M.A. Opritova, “On the initial-value problem for the Kawahara equation”, Journal of Mathematical Sciences, 201:5 (2014), 614–633
38.
A. V. Faminskii, R. V. Kuvshinov, “Initial-boundary value problems for the generalized Kawahara equation”, Russian Math. Surveys, 66:4 (2011), 819–821
39.
Andrei V. Faminskii, Nikolai A. Larkin, “Odd-order quasilinear evolution equations posed on a bounded interval”, Bol. Soc. Paranaense Mat. (3s.), 28:1 (2010), 67–77
Andrei V. Faminskii, Nikolai A. Larkin, “Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval”, Electronic Journal of Differential Equations, 2010:1 (2010), 1–20
41.
K. Sangare, A. V. Faminskii, “Weak Solutions of a Mixed Problem in a Half-Strip for a Generalized Kawahara Equation”, Math. Notes, 85:1 (2009), 90–100
42.
R. V. Kuvshinov, A. V. Faminskii, “Mixed problem for the Kawahara equation in a half-strip”, Differential Equations, 45:3 (2009), 404–415
43.
A. V. Faminskii, “Cauchy Problem for the Korteweg–de Vries Equation in the Case of a Nonsmooth Unbounded Initial Function”, Math. Notes, 83:1 (2008), 107–115
44.
Andrei V. Faminskii, “Well-posed initial-boundary value problems for the Zakharov–Kuznetsov equation”, Electronic Journal of Differential Equations, 2008:127 (2008), 1–23
45.
Andrei V. Faminskii, Irina Yu. Bashlykova, “Weak solutions to one initial-boundary value problem with three boundary conditions for quasilinear evolution equations of the third order”, Ukranian Mathematical Bulletin, 5:1 (2008), 83–98
46.
A. V. Faminskii, “Global well-posedness of two initial–boundary-value problems for the Korteweg–de Vries equation”, Differential Integral Equations, 20:6 (2007), 601–642
47.
A. V. Faminskii, E. S. Baykova, “Weak solutions to a mixed problem with two boundary conditions for the generalized Kawahara equation”, Nonclassical equations of mathematical physics, Proc. Int. Conf. “Differential Equations, Function Theory and Applications”, dev. 100-th anniv. acad. I. N. Vekua (Novosibirsk, May 28 – June 2, 2007), eds. A. I. Kozhanov, Inst. Math. Siberian Branch Acad. Sci., Novosibirsk, 2007, 298–306
48.
Andrei V. Faminskii, “Quasilinear evolution equations of the third order”, Bol. Soc. Paranaense Mat. (3s.), 25:1-2 (2007), 91–108
49.
A. V. Faminskii, “Nonlocal well-posedness of the mixed problem for the Zakharov–Kuznetsov equation”, Journal Math. Sci., 147:1 (2007), 6524–6537
50.
A. V. Arutyunov, V. L. Kamynin, V. A. Trenogin, S. V. Uspenskii, A. V. Faminskii, E. F. Mishchenko, “Maslennikova Vera Nikolaevna”, Modern mathematical education and problems of the history and methodolody of mathematics, Int. Sci. Conf 6-th Rus. School History Math. (Tambov, September 11–15, 2006), eds. A. A. Artemov, Pershin R. V. Publ., Tambov, 2006, 28–32
51.
A. V. Faminskii, “An initial boundary-value problem in a half-strip for the Korteweg–de Vries equation in fractional-order Sobolev spaces”, Comm. Partial Differential Equations, 29:11–12 (2004), 1653–1695
52.
A. V. Faminskii, “On two initial boundary value problems for the generalized KdV equation”, Nelineinye granichnye zadachi (Nonlinear Boundary Value Problems), 14 (2004), 58–71
53.
A. V. Faminskii, “On the mixed problem for quasilinear equations of the third order”, Journal Math. Sci., 110:2 (2002), 2476–2507
A. V. Faminskii, “On nonlocal well-posedness of mixed problem in a half-strip for the generalized Korteweg-de Vries equation”, Math. Modelling, 13:12 (2001), 115–125
55.
A. V. Faminskii, “On an initial boundary value problem in a bounded domain for the generalized Korteweg–de Vries equation”, Functional Differential Equations, 8:1-2 (2001), 183–194
56.
A. V. Faminskii, “On a mixed problem in a half-strip with two boundary conditions for the generalized Korteweg–de Vries equation”, Bulletin Peoples' Friendship Univ. Russia, ser. math., 8:2 (2001), 114–127
57.
A. V. Faminskii, “On mixed problems for the generalized Korteweg–de Vries equation”, Complex analysis, differential equations and related problems, Proc. Int. Conf. (Ufa, 2000), Part II, Differential Equations, eds. L. A. Kalyakin, Inst. Math. with Comp. Center Acad. Sci., Ufa, 2000, 146–150
58.
A. V. Faminskii, “Mixed problems for the Korteweg–de Vries equation”, Sb. Math., 190:6 (1999), 903–935
59.
A. V. Faminskii, “Generalized solutions to a mixed problem in a half-strip for the Korteweg–de Vries equation”, Bulletin Peoples' Friendship Univ. Russia, ser. math., 6:1 (1999), 191–215
60.
A. V. Faminskii, “On mixed problems for the Korteweg–de Vries equation with irregular boundary data”, Dokl. Math., 59:3 (1999), 366–367
61.
A. V. Faminskii, “Nonlocal well-posedness of a mixed problem in a half-strip for the Korteweg–de Vries equation”, Vestnik Ros. un-ta druzhby narodov, ser. matem. (Bulletin Peoples' Friendship Univ. Russia, ser. math.), 3:1 (1996), 156–176
62.
A. V. Faminskii, “Nonlocal well-posedness of boundary value problems for the Korteweg–de Vries equationand its generalizations”, Materials Int. Conf. and Chebyshev readings dev. 175-th anniv. P.L.Chebyshev, Vol. 2, Moscow Lomonosov Univ., Moscow, 1996, 341–344
63.
A. V. Faminskii, “Nonlocal solutions of the Cauchy problem for the Kadomtsev–Petviashvili I equation”, Bulletin Peoples' Friendship Univ. Russia, ser. math., 2:1 (1995), 155–170
64.
A. V. Faminskii, “The Cauchy problem for the Zakharov–Kuznetsov equation”, Differential Equations, 31:6 (1995), 1002–1012
65.
Andrei V. Faminskii, “On the Cauchy problem for certain multidimensional generalizations of the KdV equation”, Memorias Esquela de Verano (Proceedings of the Summer School), Geometría Differential, Análisis Numérico and Ecuaciones Diferenciales Parciales (Differential Geometry, Numerical Analysis and Partial Differential Equations) (Medellín, July 25 – August 6, 1994), eds. J. B. Cossio, Univ. Nac. Colombia Sede Medellín (Nat. Univ. Colombia, Branch Medellín), Medellín, 1994, 15–26
66.
A. V. Faminskii, “Cauchy problem for the generalized Kadomtsev–Petviashvili equation”, Siberian Math. Journal, 33:1 (1992), 133–143
67.
A. V. Faminskii, “The Cauchy problem for the Kadomtsev–Petviashvili equation”, Russian Math. Surveys, 45:1 (1990), 203–204
68.
A. V. Faminskii, “The Cauchy problem for odd-order quasilinear equations”, Math. USSR-Sb., 68:1 (1991), 31–59
69.
A. V. Faminskii, “Cauchy problem for the Korteweg–de Vries equation and its generalizations”, Journal Math. Sci, 50:1 (1990), 1381–1420
70.
A. V. Faminskii, “A mixed problem in a half-strip for the Korteweg–de Vries equation and its generalizations”, Trans. Moscow. Math. Soc., 1989, 53–91
71.
S. N. Kruzhkov, A. V. Faminskii, “Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation”, Math. USSR-Sb., 48:2 (1984), 391–421
72.
S. N. Kruzhkov, A. V. Faminskii, “On continuity properties of solutions of some classes of nonstationary equations”, Vestnik Mosk. Univ., ser. Math., 38:3 (1983), 29–36
73.
A. V. Faminskii, “On Cauchy problem and a mixed problem in a half-strip for equations of Korteweg–de Vries type”, Dynamical problems of mechanics of continuum media, Dynamics of continuum media, 63, eds. V. N. Monakhov, Inst. Hydrodynamics Siberian Branch Acad. Sci. USSR, Novosibirsk, 1983, 152–158
74.
S. N. Kruzhkov, A. V. Faminskii, “Generalized solutions to Cauchy problem for Burgers and Korteweg–de Vries equations”, General theory of boundary problems, eds. I. V. Skrypnik, Scientific Idea, Kiev, 1983, 94–101
75.
A. V. Faminskii, “The Cauchy problem for the Korteweg–de Vries equation when the initial data are irregular”, Russian Math. Surveys, 36:3 (1981), 248–249
76.
S. N. Kruzhkov, A. V. Faminskii, “Generalized solutions of the Korteweg–de Vries equation”, Soviet Math. Dokl., 24:3 (1981), 676–679
Thesis
77.
A. V. Faminskii, Boundary value problems for Korteweg–de Vries equation and ita generalizations, Thesis DrSc phys., math., Moscow Lomonosov Univ., Moscow, 2001 , 333 pp.
78.
A. V. Faminskii, Cauchy problem and a mixed problem in a half-strip for equations of Korteweg–de Vries type, Thesis PhD phys., math., Moscow Lomonosov Univ., Moscow, 1984 , 147 pp.
Popular science or education materials
79.
A. V. Faminskii, Selected chapters of the theory of evolution equations, Peoples' Friendship Univ. Russia, Moscow, 2014 , 163 pp., textbook
80.
A. V. Faminskii, Functional spaces of evolutional type, Peoples' Friendship Univ. Russia, Moscow, 2011 , 144 pp., textbook
81.
Andrei V. Faminskii, Evolution Functional Spaces. The basis of the theory, Lambert Academic Publishing, Saarbrücken, Germany, 2011 , 81 pp.
Personalia
82.
N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Russian Math. Surveys, 53:5 (1998), 1071–1078
Manuscripts
83.
Andrei V. Faminskii, Initial-boundary value problems for quasilinear evolution equations of an odd order, Lectures, III Encontro Nacional de Analise Matemática e Aplicações (III Nat. Meeting Math. Anal. Appl.), Maringá, Brazil, November 18–20, 2009, 38 p., 2009
84.
A. V. Faminskii, On a mixed problem in a half-strip for equations of Korteweg–de Vries type, Dep. in VINITI № 8046-85, 10 p., 1985
85.
A. V. Faminskii, Solvability of a mixed problem in a half-strip and Cauchy problem for equations of Korteweg–de Vries type, Dep. in VINITI № 4291-83, 31 p., 1983
Direct and inverse problems for odd-order quasilinear evolution equations A. V. Faminskii III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 8, 2023 18:25
