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Chechkin, Gregory Aleksandrovich

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Total publications: 35
Scientific articles: 29
Presentations: 4

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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
Phone: +7 (499) 613 45 35
Fax: +7 (495) 939 20 90
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
2019
1. 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; J. Math. Sci. (N. Y.), 244:2 (2020), 158–169  scopus
2018
2. 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  elib; Izv. Math., 82:6 (2018), 1108–1135  isi  scopus
2016
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. G. A. Chechkin, E. A. Pichugina (Akimova), “On Weighted Korn's Inequality for a Thin Nonsymmetric Plate”, Tr. Mat. Inst. Steklova, 236 (2002),  347–353  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 334–340
21. E. I. Doronina, G. A. Chechkin, “On Eigenvibrations of a Body with Many Concentrated Masses Located Nonperiodically along the Boundary”, Tr. Mat. Inst. Steklova, 236 (2002),  158–166  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 236 (2002), 148–156
2001
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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 Boundary Layers of a Rheologically Complex Fluid
G. A. Chechkin
International conference "Classical mechanics, dynamical systems and mathematical physics" on the occasion of Academician Valery V. Kozlov's 70th birthday
January 23, 2020 15:45
2. О влиянии концентрированных масс на колебание густого каскадного соединения
G. A. Chechkin
Differential geometry and applications
October 22, 2018 16:45
3. О густом каскадном соединении с концентрированными массами
G. A. Chechkin

May 14, 2018 16:45
4. 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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