Petrova Yu., Tikhomirov S., Efendiev Ya.
Propagating terrace in a two-tubes model of gravitational fingering
SIAM Journal on Mathematical Analysis, 57 (2025), 30-64.
doi arXiv
Monakov G., Tikhomirov S.
Probabilistic shadowing in linear skew products.
Discrete and Continuous Dynamical Systems, 45 (2025), 391-409.
doi arXiv
Apushkinskaya D., Tikhomirov S., Uraltseva N.
Properties of the phase boundary in the parabolic problem with hysteresis.
Zapiski Nauchnykh Seminarov POMI 536 (2024), 26-53.
pdf arXiv:2411.17512
Bakharev F., Enin A., Matveenko S., Pavlov D., Petrova Yu., Rastegaev N., Tikhomirov S.
Velocity of viscous fingers in miscible displacement: Intermediate concentration.
J. Comput. Appl. Math., 451 (2024), 116107.
doi arXiv
Tikhomirov S., Shalgin V.
Convergence rate of algorithms for solving linear equations by quantum annealing.
Comput. Math. and Math. Phys. 64 (2024), 989–1003.
doi arXiv
Priezzhev V., Priezzhev P., Tikhomirov S.
Probabilistic shadowing for pseudotrajectories with decreasing errors.
Zapiski Nauchnykh Seminarov POMI 505 (2021), 207-229.
Journal of Mathematical Sciences 281 (2024), 142-157.
doi
Starkov I.A., Pavlov D.A., Tikhomirov S., Bakharev F.L.
The non-monotonicity of growth rate of viscous fingers in heterogeneous porous media.
Comput Geosci 27 (2023), 783–792.
doi arXiv
Bakharev F., Enin A., Kalinin K., Petrova Yu., Rastegaev N., Tikhomirov S.
Optimal polymer slugs injection profiles.
J. Comput. Appl. Math. 425 (2023), 115042.
doi arXiv
Bakharev F., Enin A., Groman A., Kalyuzhnyuk A., Matveenko S., Petrova Yu., Starkov I., Tikhomirov S.
Velocity of viscous fingers in miscible displacement: Comparison with analytical models.
J. Comput. Appl. Math. 402 (2022), 113808.
doi arXiv
Enin A., Perstneva P., Tikhomirov S.
Periodic solutions of parabolic equations with hysteresis in dimension 1.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 489 (2020), 48, 36–54.
Journal of Mathematical Sciences 260 (2022), 21-32.
doi
Tikhomirov S., Bakharev F., Groman A., Kalyuzhnyuk A., Petrova Yu., Enin A., Kalinin K., Rastegaev N.
Calculation of Graded Viscosity Banks Profile on the Rear End of the Polymer Slug.
SPE Russian Petroleum Technology Conference (2021), SPE-206426-MS.
doi
Bakharev, F., Campoli, L., Enin, A., Matveenko, S., Petrova, Y., Tikhomirov, S., Yakovlev, A.
Numerical investigation of viscous fingering phenomenon for raw field data.
Transp. Porous Media 132 (2020), no. 2, 443–464.
doi
Monakov G., Tikhomirov S., Yakovlev A.
Displacement of Viscous Fluids in a Set of Parallel Pipes.
Comput. Math. Math. Phys. 60 (2020), no. 3, 484–497.
doi arXiv
Gurevich P., Tikhomirov S.
Spatially discrete reaction-diffusion equations with discontinuous hysteresis.
Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 4, 1041–1077.
doi arXiv
Scheel A., Tikhomirov S.
Depinning asymptotics in ergodic media.
Patterns of dynamics, 88–108, Springer Proc. Math. Stat., 205 (2017), Springer, Cham.
doi arXiv
Gurevich P., Tikhomirov S.
Rattling in spatially discrete diffusion equations with hysteresis.
Multiscale Model. Simul. 15 (2017), no. 3, 1176–1197.
doi arXiv
Fisher, T., Petty, T., Tikhomirov, S.
Nonlocally maximal and premaximal hyperbolic sets.
Modern theory of dynamical systems, 83–99, Contemp. Math., 692 (2017), Amer. Math. Soc., Providence, RI.
book arXiv
Tikhomirov S.
On absolute nonshadowability of transitive maps.
Differ. Uravn. Protsessy Upr. (2016), no. 3, 57–65.
pdf arXiv
Curran M., Gurevich P., Tikhomirov S.
Recent advance in reaction-diffusion equations with non-ideal relays.
Control of self-organizing nonlinear systems, 211–234, Underst. Complex Syst., Springer, [Cham], 2016.
doi arXiv
Tikhomirov S.
An example of a vector field with the oriented shadowing property.
Journal of Dynamics and Control Systems, 21 (2015), no. 4, 643-654.
doi arXiv
Tikhomirov S.
Shadowing in linear skew products.
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 432 (2015), 261-273.
doi arXiv
Gan S., Li M., Tikhomirov S.
Oriented shadowing property and $\Omega$-stability for vector fields.
J. Dynam. Differential Equations 28 (2016), no. 1, 225–237.
doi arXiv
Tikhomirov S.
Holder Shadowing on Finite Intervals.
Ergodic Theory and Dynamical Systems, 35 (2015), no. 06, pp. 2000-2016.
doi arXiv
Gurevich P., Tikhomirov S.
Systems of reaction-diffusion equations with spatially distributed hysteresis.
Mathematica Bohemica 139 (2014), No. 2, pp. 239-257.
pdf arXiv
Osipov A.V., Tikhomirov S.
Shadowing in actions of finitely-generated groups.
Dyn. Syst. 29 (2014), no. 3, 337-351.
doi arXiv
Kryzhevich S., Tikhomirov S.
Partial hyperbolicity and central shadowing.
Discrete and Continuous Dynamical Systems -- A 33 (2013), 2901-2909.
doi arXiv
Gurevich P., Shamin R., Tikhomirov S.
Reaction-diffusion equations with spatially distributed hysteresis.
SIAM J. Math. Anal. 45 (2013), no. 3, 1328-1355.
doi arXiv
Gurevich P., Tikhomirov S.
Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis.
Nonlinear Anal. 75 (2012) 6610-6619.
doi arXiv
Palmer K., Pilyugin S., Tikhomirov S.
Lipschitz shadowing and structural stability of flows.
J. Differential Equations 252 (2012) 1723-1747.
doi arXiv
Gurevich P., Tikhomirov S.
Symmetric periodic solutions of parabolic problems with hysteresis.
Journal of Dynamics and Differential Equations 23 (2011) 923-960.
doi arXiv
Pilyugin S. , Tikhomirov S.
Lipschitz Shadowing implies structural stability.
Nonlinearity 23 (2010) 2509-2515.
doi arXiv
Pilyugin S., Osipov A., Tikhomirov S.
Periodic Shadowing and $\Omega$-stability.
Regul. Chaotic Dyn. 15 (2010), no. 2-3, 404-417.
doi arXiv
Pilyugin S., Tikhomirov S.
Vector fields with the oriented shadowing property.
J. Diff. Eq. 2010 Vol. 248. pp. 1345-1375.
doi arXiv
Pilyugin S. , Tikhomirov S.
Sets of vector fields with various shadowing properties of pseudotrajectories.
Doklady RAN. 2008. Vol. 422. N. 1. p. 30-31.
doi arXiv
Tikhomirov S.
Interiors of sets of vector fields corresponding to some classes of reparametrizations.
Vestnik St. Peterburg Univ. Math. Ser. 1, 2008, N4, p. 90-97.
doi arXiv
Tikhomirov S.
A method for investigation of a neighborhood of a nontransverse homoclinic point of a two-dimensional diffeomorphism.
Diff. Equat. and Control Processes. 2006, N1, p. 48-77.
pdf
Pilyugin S. , Tikhomirov S.
Shadowing in actions of some Abelian groups.
Fund. Math. 2003 Vol. 179. pp. 83-96.
doi
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