Publications

1. Petrova Yu., Tikhomirov S., Efendiev Ya.
   Propagating terrace in a two-tubes model of gravitational fingering
   arXiv:2401.05981

2. Bakharev F., Enin A., Matveenko S., Rastegaev N., Pavlov D., Tikhomirov S.
   Relation between size of mixing zone and intermediate concentration in miscible displacement.
   arXiv:2310.14260

3. Shalgin V., Tikhomirov S.
   Convergence rate of algorithms for solving linear equations by quantum annealing.
   accepted  by Computational Mathematics and Mathematical Physics
   arXiv:2310.15441

4. Monakov G., Tikhomirov S.
   Probabilistic shadowing in linear skew products.
   arXiv:2012.08264

5. 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

6. 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

7. 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

8. 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

9. Priezzhev V., Priezzhev P., Tikhomirov S.
   Probabilistic shadowing for pseudotrajectories with decreasing errors.
   Zapiski Nauchnykh Seminarov POMI 505 (2021), 207-229.

10. 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

11. 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

12. 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), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 48, 36–54.
    doi

13. 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

14. Scheel A., Tikhomirov S.
    Depinning asymptotics in ergodic media.
    Patterns of dynamics, 88–108, Springer Proc. Math. Stat., 205 (2017), Springer, Cham.
    doi     arXiv

15. Gurevich P., Tikhomirov S.
    Rattling in spatially discrete diffusion equations with hysteresis.
    Multiscale Model. Simul. 15 (2017), no. 3, 1176–1197.
    doi     arXiv

16. 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.
    arXiv

17. Tikhomirov S.
    On absolute nonshadowability of transitive maps.
    Differ. Uravn. Protsessy Upr. (2016), no. 3, 57–65.
    pdf     arXiv

18. 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

19. 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 

20. Tikhomirov S.
    Shadowing in linear skew products.
    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 432 (2015), 261-273.
    doi     arXiv

21.  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

22. Tikhomirov S.
    Holder Shadowing on Finite Intervals.
    Ergodic Theory and Dynamical Systems, 35 (2015), no. 06, pp. 2000-2016.
    doi     arXiv

23. Gurevich P., Tikhomirov S.
    Systems of reaction-diffusion equations with spatially distributed hysteresis.
    Mathematica Bohemica 139 (2014), No. 2, pp. 239-257.
    pdf     arXiv

24. Osipov A.V., Tikhomirov S.
    Shadowing in actions of finitely-generated groups.
    Dyn. Syst. 29 (2014), no. 3, 337-351.
    doi     arXiv

25. Kryzhevich S., Tikhomirov S.
    Partial hyperbolicity and central shadowing.
    Discrete and Continuous Dynamical Systems -- A 33 (2013), 2901-2909.
    doi     arXiv

26. 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

27. Gurevich P., Tikhomirov S.
    Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis.
    Nonlinear Anal. 75 (2012) 6610-6619.
    doi     arXiv

28. Palmer K., Pilyugin S., Tikhomirov S.
    Lipschitz shadowing and structural stability of flows.
    J. Differential Equations 252 (2012) 1723-1747.
    doi     arXiv

29. Gurevich P., Tikhomirov S.
    Symmetric periodic solutions of parabolic problems with hysteresis.
    Journal of Dynamics and Differential Equations 23 (2011) 923-960.
    doi     arXiv

30. Pilyugin S. , Tikhomirov S.
    Lipschitz Shadowing implies structural stability.
    Nonlinearity 23 (2010) 2509-2515.
    doi     arXiv

31. Pilyugin S., Osipov A., Tikhomirov S.
    Periodic Shadowing and $\Omega$-stability.
    Regul. Chaotic Dyn. 15 (2010), no. 2-3, 404-417.
    doi     arXiv

32. Pilyugin S., Tikhomirov S.
    Vector fields with the oriented shadowing property.
    J. Diff. Eq. 2010 Vol. 248. pp. 1345-1375.
    doi     arXiv

33. 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

34. 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

35. 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

36.  Pilyugin S. , Tikhomirov S.
    Shadowing in actions of some Abelian groups.
    Fund. Math. 2003 Vol. 179. pp. 83-96.
    doi

Popularization 

1. Tikhomirov S.
   Hysterese
   Forschungsbericht 2014 - Max-Planck-Institut für Mathematik in den Naturwissenschaften.
   Link 

2.  Petrov F., Tikhomirov S.
   About angles and distances.
   St. Petersburg high-school mathematical Olympiads 2000-2002 Nauka (RAN), St. Petersburg (2006) pp. 330-348.
   pdf