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).
Main publications:
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]
[Sistemnoe matematicheskoe modelirovanie protsessov vodoobmena] 