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Chechkin, Gregory Aleksandrovich

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Total publications: 36
Scientific articles: 30
Presentations: 7

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Chechkin, Gregory Aleksandrovich
Professor
Doctor of physico-mathematical sciences (2007)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 7.06.1966
E-mail:
Website: http://abris.tv/grisha
Keywords: homogenization of differential operators; spectral theory of differential operators; asymptotic methods; integral estimates of solutions of PDE; behavior of thin plates, rod structures and junctions; microinhomogenious media.
UDC: 517.9, 517.946, 517.95, 517.956.2, 517.956.225, 517.956.226, 517.956.6, 517.956.8, 517.98, 517.984.4, 517.984.6, 519.632.4, 517.955.8
MSC: 35b20, 35b27, 35b40, 35b45, 35c20, 35j05, 35j25, 35m10, 35p15, 74b99, 74k10, 74k15, 74k20, 74k30, 74q99, 35J25, 35B25, 39A10, 39A11, 39A70, 39B62, 41A44, 45A05

Subject:

Boundary homogenization for PDE in domains with microinhomogeneous structure. There were formulated and proved homogenization Theorems for boundary value problems with rapidly changing type of boundary conditions with periodic and nonperiodic boundary conditions. Also there were obtained the estimates of deviation of solutions of initial problem from solutions of homogenizaed problem. Vibration of thin plates, rods and junctions. Vibration of thin nonsymmetric plates with rough surface and other singular constructions were described. Weighted Korn type inequality for such domains were proved. Homogenization of random structures. We gave new definition of domains with random structure and proved homogenization theroems. Domains with oscillating boundary. We studied the behavior of bodies with the oscillation of external boundary and internal perforation. Also there were proved homogenization theorems and were constructed leading terms of the asymptotic expansion of solutions with respect to the small parameter characterized the microinhomogenity.Singular Measures and homogenization. We introduced new approach to homogenization problems in domains with thin and infinitisimally thin elements. We define the Sobolev function-spaces, proved the embedding theorems and Weyl-type theorems. Also we proved homogenization theorems for such structures.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1988 (department of differential equations). Ph.D. thesis was defended in 1992 (scientific advisor — academitioan professor Olga Oleinik). Doctor of Mathematics (habilitation) in 2007. A list of my works contains more than 110 titles (including two monographs). Since 1994 I have led the research seminar at MSU on homogenization theory. I was an invited professor in few universities (France, Italy, Japan, Norway, Spain, USA). I am a scientific advisor of graduate students.

First place in Young Scientists Competition, 1988, Moscow State University. I won the competition in Moscow State University and became the International Research Scholar — MUSSIA (Indiana University, Bloomington, 1990.) Prize winner of the french PRO MATHEMATICA grants for Young Scientists (1992–1994, 1996–1998). I gave more then 10 plenary and invited lectures at international conferences and congresses.

   
Main publications:
  • The Boundary Value Problem in Domains with Very Rapidly Oscillating Boundary (jointly with A. Friedman and A. L. Piatnitski) // Journal of Mathematical Analysis and Applications (JMAA), 1999, v. 231, no. 1, p. 213–234.
  • Effective Membrane Permeability: Estimates and Low Concentration Asymptotics (Jointly with A. G. Belyaev and R. R. Gadylshin) // SIAM J. Appl. Math., 2000, v. 60, no. 1, p. 84–108.

http://www.mathnet.ru/eng/person8304
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/314038

Publications in Math-Net.Ru
2020
1. R. R. Bulatova, V. N. Samokhin, G. A. Chechkin, “On an Unsteady Boundary Layer of a Viscous Rheologically Complex Fluid”, Trudy Mat. Inst. Steklova, 310 (2020),  40–77  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 310 (2020), 32–69  isi  scopus
2019
2. R. R. Bulatova, V. N. Samokhin, G. A. Chechkin, “Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019),  72–90  mathnet  elib; J. Math. Sci. (N. Y.), 244:2 (2020), 158–169  scopus
2018
3. R. R. Gadyl'shin, A. L. Piatnitski, G. A. Chechkin, “On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type”, Izv. RAN. Ser. Mat., 82:6 (2018),  37–64  mathnet  mathscinet  elib; Izv. Math., 82:6 (2018), 1108–1135  isi  scopus
2016
4. V. N. Samokhin, G. A. Chechkin, “Equations of boundary layer for a generalized newtonian medium near a critical point”, Tr. Semim. im. I. G. Petrovskogo, 31 (2016),  158–176  mathnet; J. Math. Sci. (N. Y.), 234:4 (2018), 485–496  scopus
5. S. T. Erov, G. A. Chechkin, “Vibrations of a fluid containing a wide spaced net with floats under its free surface”, Tr. Semim. im. I. G. Petrovskogo, 31 (2016),  38–62  mathnet; J. Math. Sci. (N. Y.), 234:4 (2018), 407–422  scopus
2015
6. T. A. Mel'nik, G. A. Chechkin, “Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses”, Izv. RAN. Ser. Mat., 79:3 (2015),  41–86  mathnet  mathscinet  zmath  elib; Izv. Math., 79:3 (2015), 467–511  isi  scopus
2014
7. I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, N. A. Izobov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. V. Palin, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, E. V. Radkevich, O. S. Rozanova, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Scientific heritage of Vladimir Mikhailovich Millionshchikov”, Tr. Semim. im. I. G. Petrovskogo, 30 (2014),  5–41  mathnet; J. Math. Sci. (N. Y.), 210:2 (2015), 115–134
2013
8. A. Yu. Linkevich, S. V. Spiridonov, G. A. Chechkin, “Homogenization of stratified dilatant fluid”, CMFD, 48 (2013),  75–83  mathnet; Journal of Mathematical Sciences, 202:6 (2014), 849–858  scopus
2011
9. G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, P. Wall, “A new weighted Friedrichs-type inequality for a perforated domain with a sharp constant”, Eurasian Math. J., 2:1 (2011),  81–103  mathnet  mathscinet  zmath
10. V. N. Samokhin, G. M. Fadeeva, G. A. Chechkin, “Equations of the boundary layer for a modified Navier-Stokes system”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  329–361  mathnet  zmath  elib; J. Math. Sci. (N. Y.), 179:4 (2011), 557–577  scopus
11. A. Yu. Linkevich, S. V. Spiridonov, G. A. Chechkin, “On boundary layer of Newtonian fluid, flowing on a rough surface and percolating through a perforated obstacle”, Ufimsk. Mat. Zh., 3:3 (2011),  93–104  mathnet  zmath
12. R. R. Gadyl'shin, Yu. O. Koroleva, G. A. Chechkin, “On the asymptotics of a solution of a boundary value problem in a domain perforated along boundary”, Vestnik Chelyabinsk. Gos. Univ., 2011, 14,  27–36  mathnet
2009
13. T. A. Mel'nik, G. A. Chechkin, “Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions”, Mat. Sb., 200:3 (2009),  49–74  mathnet  mathscinet  zmath  elib; Sb. Math., 200:3 (2009), 357–383  isi  scopus
2006
14. Y. Amirat, G. A. Chechkin, R. R. Gadyl'shin, “Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with oscillating boundary”, Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006),  102–115  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 46:1 (2006), 97–110  scopus
2005
15. G. A. Chechkin, “Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case”, Izv. RAN. Ser. Mat., 69:4 (2005),  161–204  mathnet  mathscinet  zmath  elib; Izv. Math., 69:4 (2005), 805–846  isi  elib  scopus
2004
16. G. A. Chechkin, “Estimation of Solutions of Boundary-Value Problems in Domains with Concentrated Masses Located Periodically along the Boundary: Case of Light Masses”, Mat. Zametki, 76:6 (2004),  928–944  mathnet  mathscinet  zmath; Math. Notes, 76:6 (2004), 865–879  isi  scopus
17. G. A. Chechkin, “Splitting of a multiple eigenvalue in a problem on concentrated masses”, Uspekhi Mat. Nauk, 59:4(358) (2004),  205–206  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:4 (2004), 790–791  isi  scopus
2003
18. V. A. Kondratiev, G. A. Chechkin, “On the Asymptotics of Solutions of the Lavrent'ev–Bitsadze Equation in a Partially Perforated Domain”, Differ. Uravn., 39:5 (2003),  645–655  mathnet  mathscinet; Differ. Equ., 39:5 (2003), 681–693
2002
19. V. A. Kondratiev, G. A. Chechkin, “Homogenization of the Lavrent'ev–Bitsadze Equation in a Partially Perforated Domain”, Differ. Uravn., 38:10 (2002),  1390–1396  mathnet  mathscinet; Differ. Equ., 38:10 (2002), 1481–1487
20. M. E. Perez, G. A. Chechkin, E. I. Yablokova, “On eigenvibrations of a body with “light” concentrated masses on the surface”, Uspekhi Mat. Nauk, 57:6(348) (2002),  195–196  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:6 (2002), 1240–1242  isi  scopus
21. G. A. Chechkin, E. A. Pichugina (Akimova), “On Weighted Korn's Inequality for a Thin Nonsymmetric Plate”, Trudy Mat. Inst. Steklova, 236 (2002),  347–353  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 334–340
22. E. I. Doronina, G. A. Chechkin, “On Eigenvibrations of a Body with Many Concentrated Masses Located Nonperiodically along the Boundary”, Trudy Mat. Inst. Steklova, 236 (2002),  158–166  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 148–156
2001
23. A. G. Belyaev, A. L. Piatnitski, G. A. Chechkin, “Averaging in a perforated domain with an oscillating third boundary condition”, Mat. Sb., 192:7 (2001),  3–20  mathnet  mathscinet  zmath  elib; Sb. Math., 192:7 (2001), 933–949  isi  scopus
24. E. I. Doronina, G. A. Chechkin, “On the averaging of solutions of a second-order elliptic equation with nonperiodic rapidly changing boundary conditions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, 1,  14–19  mathnet  mathscinet  zmath
1999
25. A. Yu. Belyaev, G. A. Chechkin, “Averaging of operators with a fine-scaled structure of boundary conditions”, Mat. Zametki, 65:4 (1999),  496–510  mathnet  mathscinet  zmath; Math. Notes, 65:4 (1999), 418–429  isi
26. R. R. Gadyl'shin, G. A. Chechkin, “A boundary value problem for the Laplacian with rapidly changing type of boundary conditions in a multi-dimensional domain”, Sibirsk. Mat. Zh., 40:2 (1999),  271–287  mathnet  mathscinet  zmath; Siberian Math. J., 40:2 (1999), 229–244  isi
1998
27. A. G. Belyaev, A. L. Piatnitski, G. A. Chechkin, “Asymptotic behavior of the solution of a boundary value problem in a punctured domain with an oscillating boundary”, Sibirsk. Mat. Zh., 39:4 (1998),  730–754  mathnet  mathscinet  zmath; Siberian Math. J., 39:4 (1998), 621–644  isi
1995
28. A. G. Belyaev, G. A. Chechkin, “Homogenization of a mixed boundary-value problem for the Laplace operator in the case of an insoluble 'limit' problem”, Mat. Sb., 186:4 (1995),  47–60  mathnet  mathscinet  zmath; Sb. Math., 186:4 (1995), 511–525  isi
1993
29. O. A. Oleinik, G. A. Chechkin, “On boundary-value problems for elliptic equations with rapidly changing type of boundary conditions”, Uspekhi Mat. Nauk, 48:6(294) (1993),  163–164  mathnet  mathscinet  zmath; Russian Math. Surveys, 48:6 (1993), 173–175  isi
30. G. A. Chechkin, “Averaging of boundary value problems with a singular perturbation of the boundary conditions”, Mat. Sb., 184:6 (1993),  99–150  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 79:1 (1994), 191–222  isi

2011
31. M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011),  5–10  mathnet  mathscinet; Journal of Mathematical Sciences, 190:1 (2013), 1–7
32. I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. Yu. Goritskii, N. V. Denisova, V. V. Zhikov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Olga Arsenjevna Oleinik”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  5–7  mathnet  elib; J. Math. Sci. (N. Y.), 179:3 (2011), 345–346
2007
33. I. V. Astashova, L. A. Bagirov, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007),  5–28  mathnet  mathscinet; J. Math. Sci. (N. Y.), 143:4 (2007), 3183–3197
2005
34. I. V. Astashova, L. A. Bagirov, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, O. B. Lupanov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Vladimir Aleksandrovich Kondrat'ev”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, 5,  77–79  mathnet
2003
35. T. D. Venttsel', V. S. Vladimirov, V. V. Zhikov, A. M. Il'in, V. A. Il'in, V. A. Kondrat'ev, L. D. Kudryavtsev, E. F. Mishchenko, S. M. Nikol'skii, Yu. S. Osipov, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, L. D. Faddeev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Ol'ga Arsen'evna Oleinik (obituary)”, Uspekhi Mat. Nauk, 58:1(349) (2003),  165–174  mathnet  mathscinet  zmath; Russian Math. Surveys, 58:1 (2003), 161–172  isi
2000
36. T. D. Venttsel', Yu. A. Dubinskii, A. M. Il'in, V. A. Kondrat'ev, V. P. Mikhailov, A. A. Mal'tsev, O. A. Oleinik, S. I. Pokhozhaev, N. Kh. Rozov, G. A. Chechkin, T. A. Shaposhnikova, “Anatolii Sergeevich Kalashnikov (obituary)”, Uspekhi Mat. Nauk, 55:5(335) (2000),  161–168  mathnet  mathscinet; Russian Math. Surveys, 55:5 (2000), 977–985  isi

Presentations in Math-Net.Ru
1. On the Bojarskii–Meyers estimates
G. A. Chechkin
Russian-Chinese Conference «Integrable Systems and Geometry»
December 21, 2021 13:10   
2. Оценки Мейерса для решений задачи Зарембы
G. A. Chechkin

August 9, 2021 14:30
3. On singular behaviour of spectrum for problems with concentrated masses
G. A. Chechkin
V. I. Smirnov Seminar on Mathematical Physics
April 5, 2021 16:30
4. On the Boundary Layers of a Rheologically Complex Fluid
G. A. Chechkin
International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday
January 23, 2020 15:45   
5. О влиянии концентрированных масс на колебание густого каскадного соединения
G. A. Chechkin
Differential geometry and applications
October 22, 2018 16:45
6. О густом каскадном соединении с концентрированными массами
G. A. Chechkin
Hamiltonian systems and statistical mechanics
May 14, 2018 16:45
7. Concentrated masses and "thick skin" effect
G. A. Chechkin, T. P. Chechkina
International Conference on Differential Equations and Dynamical Systems
July 5, 2014 11:50

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