Hamilton–Jacobi equation,
viscosity solutions,
singular solutions of PDEs,
nonsmooth analysis,
transport optimization.
UDC:
517.957, 517.958, 524.8, 517.972.5, 519.854.2
Subject:
Nonlinear dynamics,
Burgers equation,
Monge-Kantorovich transportation metric,
nonlinear mass transfer models in fluid dynamics and cosmology
Main publications:
K. Khanin, A. Sobolevski, “On Dynamics of Lagrangian Trajectories for Hamilton–Jacobi Equations”, Archive for Rational Mechanics and Analysis, 219 (2016), 861–885 , arXiv: 1211.7084
K. M. Khanin, D. V. Khmelev, A. N. Sobolevskii, “On the velocities of Lagrangian minimizers”, Mosc. Math. J., 5:1 (2005), 157–169
Y. Brenier, U. Frisch, M. Henon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevskii, “Reconstruction of the early Universe as a convex optimization problem”, Mon. Not. R. Astron. Soc., 346:2 (2003), 501–524 , arXiv: astro-ph/0304214
Uriel Frisch, Sabino Matarrese, Roya Mohayaee, Andrei Sobolevski, “A reconstruction of the initial conditions of the Universe by optimal mass transportation”, Nature, 417 (2002), 260–262 , arXiv: astro-ph/0109483
A. N. Sobolevskii, “Periodic solutions of the Hamilton–Jacobi equation with a periodic non-homogeneous term and Aubry–Mather theory”, Sb. Math., 190:10 (1999), 1487–1504 , arXiv: chao-dyn/9906035
G. L. Litvinov, А. Ya. Rodionov, S. Sergeev, A. N. Sobolevski, “Universal algorithms for solving discrete stationary Bellman equations”, Russian Universities Reports. Mathematics, 24:128 (2019), 393–431
2016
2.
K. Khanin, A. Sobolevski, “On Dynamics of Lagrangian Trajectories for Hamilton–Jacobi Equations”, Archive for Rational Mechanics and Analysis, 219 (2016), 861–885 , arXiv: 1211.7084
A. V. Kroshnin, A. N. Sobolevskii, “Baritsentry Freshe i zakon bolshikh chisel dlya mer na veschestvennoi pryamoi”, Trudy MFTI, 8:2 (2016), 112-125
2015
4.
Alexey Kroshnin, Andrei Sobolevski, Fréchet Barycenters and a Law of Large Numbers for Measures on the Real Line, 2015 , 17 pp., arXiv: 1512.08421
5.
Galina I. Rozhkova, Andrei N. Sobolevski, “Scientific Activity of Alfred Yarbus: The Stages of Research Work, Senior and Younger Colleagues, Conditions of Investigations”, Perception, 44:8-9 (2015), 837–850http://pec.sagepub.com/content/44/8-9/837
S. K. Nechaev, A. N. Sobolevski, O. V. Valba, “Planar diagrams from optimization for concave potentials”, Phys. Rev. E, 87 (2013), 012102 , 9 pp., arXiv: 1203.3248
Matteo Novaga, Andrei Sobolevski, Eugene Stepanov, “Droplet condensation and isoperimetric towers”, Pacific J. Math., 262:2 (2013), 457–480 (preprint: at CVGMT server)
8.
G. L. Litvinov, A. Y. Rodionov, S. N. Sergeev, A. N. Sobolevski, “Universal algorithms for solving the matrix Bellman equations over semirings”, Soft Computing, 17:10 (2013), 1767–1785 , arXiv: math/1209.5011
Julie Delon, Julien Salomon, Andrei Sobolevski, “Local Matching Indicators for Transport Problems with Concave Costs”, SIAM J. Discrete Math., 26:2 (2012), 801–827 , arXiv: 1102.1795
Julie Delon, Julien Salomon, Andrei Sobolevski, “Minimum-weight perfect matching for non-intrinsic distances on the line”, J. Math. Sci. (N. Y.), 181:6 (2012), 782–791 , arXiv: 1102.1558
2011
11.
Grigory L. Litvinov, Victor P. Maslov, Anatoly Ya. Rodionov, Andrei N. Sobolevski, “Universal Algorithms, Mathematics of Semirings and Parallel Computations”, Coping with Complexity: Model Reduction and Data Analysis, Lecture Notes in Computational Science and Engineering, 75, eds. Alexander N. Gorban, Dirk Roose, Springer, 2011, 63–89
Julie Delon, Julien Salomon, Andrei Sobolevski, “Local matching indicators for concave transport costs”, C. R. Acad. Sci. Paris Sér I, 348:15 (2010), 901–905 , arXiv: 0912.0179
Konstantin Khanin, Andrei Sobolevski, “Particle dynamics inside shocks in Hamilton–Jacobi equations”, Phil. Trans. R. Soc. A, 368:1916, Theme Issue “Turbulent Mixing and Beyond” (Snezhana I. Abarzhi and Katepalli R. Sreenivasan, eds) (2010), 1579-1593 , arXiv: 1001.0498
Julie Delon, Julien Salomon, Andrei Sobolevski, “Fast Transport Optimization for Monge Costs on the Circle”, SIAM J. Appl. Math., 70:7 (2010), 2239–2258 , arXiv: 0902.3527
A. N. Sobolevskii, “Vypuklyi analiz, tropicheskaya algebra i obrabotka astronomicheskikh dannykh”, Issledovaniya po vypuklomu analizu, Matematicheskii forum (Itogi nauki. Yug Rossii), no. 2, Yuzhnyi matematicheskii institut Vladikavkazskogo nauchnogo tsentra RAN i Pravitelstva Respubliki Severnaya Osetiya-Alaniya, Vladikavkaz, 2009, 230–233
2008
17.
Roya Mohayaee, Andrei Sobolevski, “The Monge–Ampère–Kantorovich approach to reconstruction in cosmology”, Euler Equations: 250 Years On (Aussois, June 18–23, 2007), Physica D: Nonlinear Phenomena, 237, no. 14-17, 2008, 2145–2150 , arXiv: 0712.2561
A. Andrievskii, S. Gurbatov, A. Sobolevskii, “Ballistic aggregation in symmetric and nonsymmetric flows”, J. Experimental and Theoretical Phys., 104:6 (2007), 887–896 , arXiv: nlin/0601006
20.
A. A. Kurnosov, A. N. Sobolevskiǐ, “A variational approach to the reconstruction of galactic peculiar velocities”, Moscow University Physics Bulletin, 62:3 (2007), 147–150
21.
A. N. Sobolevskii, Teoriya veroyatnostei i osnovy matematicheskoi statistiki dlya fizikov, Uchebnoe posobie po kursu lektsii, Fizicheskii fakultet MGU im. M. V. Lomonosova, Moskva, 2007 , 24 pp.
2005
22.
K. M. Khanin, D. V. Khmelev, A. N. Sobolevskii, “On the velocities of Lagrangian minimizers”, Mosc. Math. J., 5:1 (2005), 157–169
Konstantin Khanin, Dmitry Khmelev, Andrei Sobolevskii, “A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain”, Idempotent Mathematics and Mathematical Physics (Erwin Schrödinger Institute, Vienna, February 3–10, 2003), Contemporary Mathematics, 377, eds. G. L. Litvinov and V. P.Maslov, American Mathematical Society, Rhode Island, 2005, 161-179 , arXiv: math/0312395
V. I. Keilis-Borok, A. A. Soloviev, C. Allègre, A. Sobolevski, M. D. Intriligator, “Patterns of macroeconomic indicators preceding the unemployment rise in Western Europe and the USA”, Pattern Recognition, 38:3 (2005), 423–435
A. N. Sobolevskii, U. Frisch, “Application of optimal transport theory to reconstruction of the early Universe”, J. Math. Sci. (N. Y.), 133:4 (2006), 1539–1542
2003
26.
Y. Brenier, U. Frisch, M. Henon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevskii, “Reconstruction of the early Universe as a convex optimization problem”, Mon. Not. R. Astron. Soc., 346:2 (2003), 501–524 , arXiv: astro-ph/0304214
R. Mohayaee, U. Frisch, S. Matarrese, A. Sobolevskii, “Back to the primordial Universe by a Monge-Ampère-Kantorovich optimization scheme”, Astronomy & Astrophysics, 406:2 (2003), 393-401 , arXiv: astro-ph/0301641
Uriel Frisch, Sabino Matarrese, Roya Mohayaee, Andrei Sobolevski, “A reconstruction of the initial conditions of the Universe by optimal mass transportation”, Nature, 417 (2002), 260–262 , arXiv: astro-ph/0109483
G. L. Litvinov, V. P. Maslov, A. N. Sobolevskiǐ, “Idempotent mathematics and interval analysis”, Vychisl. Tekhnol., 6:6 (2001), 47–70
31.
A. Yu. Loskutov, L. G. Akinshin, A. N. Sobolevskii, “Dinamika bilyardov s periodicheski zavisyaschimi ot vremeni granitsami”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 9:4-5 (2001), 50–63
2000
32.
Grigori Litvinov, Andrei Sobolevskii, “Exact interval solutions to the discrete Bellman equation and polynomial complexity of problems in interval idempotent linear algebra”, Doklady Mathematics, 62:2 (2000), 199–201 , arXiv: math/0101041
1999
33.
A. N. Sobolevskii, “Periodic solutions of the Hamilton–Jacobi equation with a periodic non-homogeneous term and Aubry–Mather theory”, Sb. Math., 190:10 (1999), 1487–1504 , arXiv: chao-dyn/9906035
34.
A. N. Sobolevskii, “Interval arithmetic and linear algebra over idempotent semirings”, Doklady Mathematics, 60:3 (1999), 431–433
35.
A. Sobolevskii, “Aubry-Mather theory and idempotent eigenfunctions of Bellman operator”, Communications in Contemporary Mathematics, 1:4 (1999), 517–533 , arXiv: chao-dyn/9906036
A. N. Sobolevskii, “Periodic solutions of the Hamilton–Jacobi equation with a periodic forcing term”, Russian Math. Surveys, 53:6 (1998), 1375–1376
1997
37.
A. N. Sobolevskii, “The small viscosity method for one-dimensional equations of the gas dynamics type without pressure”, Doklady Mathematics, 56:2 (1997), 707–709
Opening A. Sobolevski International conference «Integrable systems and applications» in honour of M. A. Olshanetsky 80-th birthday December 11, 2018 10:40
Как математика стала технической наукой A. N. Sobolevski Mathematical Workshop of the School of Applied Mathematics and Computer Science (MIPT) February 17, 2017 18:30
2019
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