Integrated methods for investigation of problems of mathematical physics, traditionally considered as far from each other, such as classical mechanics, quantum and statistical physics and hydrodynamics, are developed. Unification of these branches is based on considering the geometrically invariant form of Newton's second law or its natural generalizations (stochastic, infinite-dimensional, etc.) as the principal equation of motion. Topological characteristics of Lefschetz and Nielsen numbers type are constructed for a broad class of maps of infinite-dimensional manifolds (locally compact, weakly compact, condensing maps of Finsler manifolds, etc.).
Biography
Graduated from Mathematics Faculty of Voronezh State University (VSU) in 1971 (department of algebra and topological methods of analysis). Ph.D. thesis was defended in 1975. D.Sci. thesis was defended in 1995. A list of my works contains more than 200 titles.
Main publications:
Gliklikh Yu. E. Ordinary and stochastic differential geometry as a tool for mathematical physics. Dordrecht: Kluwer Academic Publishers, 1996. 205 p.
Gliklikh Yu. E. Global Analysis in Mathematical Physics. Geometric and Stochastic Methods. New York: Springer-Verlag, 1997. 229 p.
Gliklikh Yu. E. Globalnyi i stokhasticheskii analiz v zadachakh matematicheskoi fiziki. M.: KomKniga, 2005. 416 s.
Gliklikh Yu.E. Global and Stochastic Analysis with Applications to Mathematical Physics. London: Springer-Verlag, 2011. 460 p.
Yu. E. Gliklikh, “On periodic solutions of differential equations with continuous right-hand sides on Lie groups”, J. Comp. Eng. Math., 11:1 (2024), 3–10
2.
Y. E. Gliklikh, “On global in time solutions of stochastic algebraic-differerential equations with forward mean derivatives”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 17:2 (2024), 96–103
2023
3.
Yu. E. Gliklikh, D. S. Sergeeva, “Models of viscous fluids generated by martingales on the groups of diffeomorphisms”, J. Comp. Eng. Math., 10:1 (2023), 3–11
2022
4.
Yu. E. Gliklikh, “Stochastic equations and inclusions with mean derivatives and their applications”, CMFD, 68:2 (2022), 191–337
Yu. E. Gliklikh, “On solvability of stochastic differential equations with osmotic velocities”, Teor. Veroyatnost. i Primenen., 65:4 (2020), 806–817; Theory Probab. Appl., 65:4 (2021), 640–647
Yu. E. Gliklikh, T. A. Shchichko, “On the completeness of stochastic flows generated by equations with current velocities”, Teor. Veroyatnost. i Primenen., 64:1 (2019), 3–16; Theory Probab. Appl., 64:1 (2019), 1–11
Yu. E. Gliklikh, N. V. Zakharov, “On global in time existence of solutions to stochastic equations with backward mean derivatives”, J. Comp. Eng. Math., 5:4 (2018), 64–69
13.
Yu. E. Gliklikh, A. V. Makarova, “Stochastic inclusions with current velocities having decomposable right-hand sides”, J. Comp. Eng. Math., 5:2 (2018), 34–43
2016
14.
Yu. E. Gliklikh, K. A. Samsonova, “On existence of solutions to stochastic differential equations with osmotic velocities”, J. Comp. Eng. Math., 3:2 (2016), 32–39
15.
Yu. E. Gliklikh, A. V. Makarova, “On existence of solutions to stochastic differential inclusions with current velocities II”, J. Comp. Eng. Math., 3:1 (2016), 48–60
S. V. Azarina, Yu. E. Gliklikh, “On the Solvability of Nonautonomous Stochastic Differential Equations with Current Velocities”, Mat. Zametki, 100:1 (2016), 3–12; Math. Notes, 100:1 (2016), 3–10
Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations in terms of current velocities of the solution II”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:3 (2016), 31–40
Yu. E. Gliklikh, N. V. Vinokurova, “The Newton–Nelson equation on fiber bundles with connections”, Fundam. Prikl. Mat., 20:3 (2015), 61–81; J. Math. Sci., 225:4 (2017), 575–589
S. V. Azarina, Yu. E. Gliklikh, “On existence of solutions to stochastic differential equations with current velocities”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 100–106
Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations in terms of current velocities of the solution”, J. Comp. Eng. Math., 1:2 (2014), 45–51
Yu. E. Gliklikh, “On global in time solutions for differential-algebraic equations”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:3 (2014), 33–39
2013
23.
Yu. E. Gliklikh, O. O. Zheltikova, “Optimal solutions for inclusions of geometric Brownian motion type with mean derivatives”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:3 (2013), 38–50
Yu. E. Gliklikh, E. Yu. Mashkov, “Stochastic Leontieff type equations and mean derivatives of stochastic processes”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:2 (2013), 25–39
Yu. E. Gliklikh, “Investigation of Leontieff Type Equations with White Noise by the Methods of Mean Derivatives of Stochastic Processes”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 13, 24–34
Yu. E. Gliklikh, “Stochastic dynamics via equations and inclusions in terms of mean derivatives and infinitesimal generators”, Theory Stoch. Process., 16(32):2 (2010), 33–43
2007
27.
Yu. E. Gliklikh, “A necessary and sufficient condition for the global-in-time existence of solutions to stochastic differential and parabolic equations on manifolds”, Fundam. Prikl. Mat., 13:8 (2007), 69–76; J. Math. Sci., 159:6 (2009), 794–798
2005
28.
Yu. E. Gliklikh, P. S. Zykov, “On the two-point boundary-value problem for equations of geodesics”, Fundam. Prikl. Mat., 11:4 (2005), 65–70; J. Math. Sci., 144:5 (2007), 4409–4412
Yu. E. Gliklikh, “New version of the Lagrange approach to the dynamics of a viscous incompressible fluid”, Mat. Zametki, 55:4 (1994), 15–24; Math. Notes, 55:4 (1994), 344–350
Yu. E. Gliklikh, “On the Lagrangian approach to the hydrodynamics of a viscous incompressible fluid”, Uspekhi Mat. Nauk, 45:6(276) (1990), 127–128; Russian Math. Surveys, 45:6 (1990), 149–150
Yu. S. Baranov, Yu. E. Gliklikh, “A mechanical connection on the group of volume-preserving diffeomorphisms”, Funktsional. Anal. i Prilozhen., 22:2 (1988), 61–62; Funct. Anal. Appl., 22:2 (1988), 133–135
Yu. S. Baranov, Yu. E. Gliklikh, “A remark on the regularity of solutions of the Euler equation in hydrodynamics”, Uspekhi Mat. Nauk, 36:5(221) (1981), 163–164; Russian Math. Surveys, 36:5 (1981), 137–138
Yu. E. Gliklikh, “A certain generalization of the Hopf–Rinow theorem on geodesics”, Uspekhi Mat. Nauk, 29:6(180) (1974), 161–162
2023
35.
Yu. E. Gliklikh, M. I. Ilolov, E. I. Nemchenko, I. V. Pavlov, M. E. Semenov, N. V. Smorodina, A. A. Chubatov, “To the anniversary of the professor Yana Isaevna Belopolskaya”, Zap. Nauchn. Sem. POMI, 526 (2023), 5–16
2019
36.
A. D. Baev, Yu. E. Gliklikh, S. A. Zagrebina, A. A. Zamyshlyaeva, S. I. Kadchenko, A. V. Keller, D. V. Kostin, N. A. Manakova, V. I. Rjazhskih, G. A. Sviridyuk, T. G. Sukacheva, “Yu.I. Sapronov. To the memory of mathematician, teacher and friend”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:1 (2019), 166–168
2008
37.
N. M. Bliznyakov, V. M. Buchstaber, Yu. E. Gliklikh, V. G. Zvyagin, A. S. Mishchenko, V. V. Obukhovskii, Yu. I. Sapronov, A. T. Fomenko, A. V. Chernavskii, “Yurii Grigor'evich Borisovich (obituary)”, Uspekhi Mat. Nauk, 63:4(382) (2008), 173–174; Russian Math. Surveys, 63:4 (2008), 767–769
1997
38.
Yu. G. Borisovich, Yu. E. Gliklikh, K. D. Élvorti, “International Conference “Stochastic and Global Analysis””, Uspekhi Mat. Nauk, 52:6(318) (1997), 211–212
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