Nonlinear PDEs and their application to continuum mechanics, Free boundary problems for nonlinear PDEs.
Mathematical models for hydrodynamics and multiphase filtration (systems of the type: water-petroleum, gas-water-petroleum).
Mathematical models of hydrological cycle (processes of mass transport in coupled flows of surface, soil and underground water).
Current Position: Senior Researcher. CMAF, University of Lisbon, Portugal. (15.06.2009–present).
01.06.2007&ndash14.06.2009, CMAF, University of Lisbon. Schólarship of FCT (FCT is Fundação para a Ciência e a Tecnologia, Portugal).
In the period 01.06.2006–31.05.2007 — Sabbatical Professor at the Department of Applied Mathematics, University Complutense, Madrid ("Programa de Visitantes Distinguidos e Investigadores Extranjeros en la UCM" financed by the Ministry of Education and Science, Spain).
Full Visiting Professor, University of Beira Interior, Portugal (04.09.1995–2007, since 01.10.2005 with remunerate 0%).
1993–2000, Senior Leading Researcher of the Filtration Department of the Lavrentiev’s Institute of Hydrodynamics of Siberian Branch of Academy of Sciences of U.S.S.R., Novosibirsk.
1992–1994, Visiting Professor, Scholarship of FICYT, University of Oviedo, Oviedo, Spain, (FICYT is Fundacion para el Fomento de Investigation Cientifica y Technologia).
1976–1993, Chairman of the Filtration Department of the Lavrentiev’s Institute of Hydrodynamics of Siberian Branch of Academy of Sciences of U.S.S.R., Novosibirsk.
1968–1976, Senior Leading Researcher of the Theoretical Department of the Lavrentiev’s Institute of Hydrodynamics of Siberian Branch of Academy of Sciences of U.S.S.R., Novosibirsk.
University of Beira Interior, Covilhã, Portugal.
1995–2005. Full Visiting Professor (full-time). University of Oviedo, Asturias, Spain.
1992–1994. Visiting Professor, (scholarshipfellow of FICYT, at the University of Oviedo, Asturias, Spain).
Novosibirsk State University, Novosibirsk, Russia.
1983–1993, Full Professor of the Chair of Theoretical Mechanics (part time), 1969–1983, Associate Professor (part-time), 1968–1969, Assistant Professor (part-time).
Antontsev S. N., Dias J. I., Shmarev S. I., Energy methods for free boundary problems: Applications to nonlinear PDEs and fluid mechanics, Progress in Nonlinear Differential Equations and their Aplications, 48, Birkhäuser Boston, Inc., Boston, MA, 2002, xii+330 pp.
Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Boundary value problems in mechanics of nonhomogeneous fluids, Studies in Mathematics and its Applications, 22, North-Holland Publishing Co., Amsterdam, 1990, xii+309 pp.
Antontsev S. N., Shmarev S.I.,, Handbook of Differential Equations, Stationary Partial Differential Equations, Vol. 3. Chapter 1, Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions, Elsevier, 2006, 110 pp. (Russian)
Antontsev S. N., Localization of solutions of degenerate equations of continuum mechanics, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Gidrodinamiki, Novosibirsk, 1986, 109 pp. (Russian) [Lokalizatsiya reshenii vyrozhdayushchikhsya uravnenii mekhaniki sploshnoi sredy]
Antontsev S. N., Epikhov G. P., Kashevarov A. A., Systematic mathematical modeling of water exchange processes, Nauka, Sibirsk. Otdel., Novosibirsk, 1986, 216 pp. (Russian) [Sistemnoe matematicheskoe modelirovanie protsessov vodoobmena]
S. N. Antontsev, I. V. Kuznetsov, “Existence of entropy measure-valued solutions for forward-backward $p$-parabolic equations”, Sib. Èlektron. Mat. Izv., 14 (2017), 774–793
S. Antontsev, S. Shmarev, “On the blow-up of solutions to anisotropic parabolic equations with variable nonlinearity”, Tr. Mat. Inst. Steklova, 270 (2010), 33–48; Proc. Steklov Inst. Math., 270 (2010), 27–42
S. N. Antontsev, S. I. Shmarev, “Extinction of Solutions of Parabolic Equations with Variable Anisotropic Nonlinearities”, Tr. Mat. Inst. Steklova, 261 (2008), 16–25; Proc. Steklov Inst. Math., 261 (2008), 11–21
S. N. Antontsev, S. I. Shmarev, “Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity”, Fundam. Prikl. Mat., 12:4 (2006), 3–19; J. Math. Sci., 150:5 (2008), 2289–2301
S. N. Antontsev, S. I. Shmarev, “On localization of solutions of elliptic equations with nonhomogeneous anisotropic degeneracy”, Sibirsk. Mat. Zh., 46:5 (2005), 963–984; Siberian Math. J., 46:5 (2005), 765–782
S. N. Antontsev, M. Shipo, “Analytic regimes with peaking in the thermistor problem”, Sibirsk. Mat. Zh., 38:5 (1997), 963–977; Siberian Math. J., 38:5 (1997), 827–841
S. N. Antontsev, A. A. Kashevarov, “Splitting according to physical properties in the problem of
interrelation between surface and underground water”, Dokl. Akad. Nauk SSSR, 288:1 (1986), 86–90
S. N. Antontsev, “On the localization of solutions of nonlinear degenerate elliptic and parabolic equations”, Dokl. Akad. Nauk SSSR, 260:6 (1981), 1289–1293
S. N. Antontsev, “A finite velocity of propagation of disturbances in multidimensional two-phase filtration-problems”, Zap. Nauchn. Sem. LOMI, 96 (1980), 3–12; J. Soviet Math., 21:5 (1983), 637–644
S. N. Antontsev, A. A. Papin, “Approximation methods of solving problems of two-phase filtration”, Dokl. Akad. Nauk SSSR, 247:3 (1979), 521–525
S. N. Antontsev, V. N. Monakhov, “Three-dimensional problems of time-dependent two-phase filtration in nonhomogeneous anisotropic porous media”, Dokl. Akad. Nauk SSSR, 243:3 (1978), 553–556
S. N. Antontsev, A. M. Meirmanov, “Questions of correctness of a model of the simultaneous motion of surface and ground waters”, Dokl. Akad. Nauk SSSR, 242:3 (1978), 505–508
S. N. Antontsev, “On a problem of M. A. Lavrent'ev”, Dokl. Akad. Nauk SSSR, 228:4 (1976), 772–775
S. N. Antontsev, “Axisymmetric problems of gas dynamics with free boundaries”, Dokl. Akad. Nauk SSSR, 216:3 (1974), 473–476
S. N. Antontsev, V. N. Monakhov, “On the solvability of a class of conjugacy problems with shift”, Dokl. Akad. Nauk SSSR, 205:2 (1972), 263–266
S. N. Antontsev, V. N. Monakhov, “Riemann–Hilbert boundary value problem with discontinuous boundary conditions for quasi-linear elliptic systems of equations”, Dokl. Akad. Nauk SSSR, 175:3 (1967), 511–513