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.
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.
Yu. A. Alkhutov, G. A. Chechkin, “On the Boyarsky–Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift”, CMFD, 70:1 (2024), 1–14
2.
Yu. A. Alkhutov, G. A. Chechkin, “Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate”, TMF, 218:1 (2024), 3–22; Theoret. and Math. Phys., 218:1 (2024), 1–18
V. N. Samokhin, G. A. Chechkin, “Nonclassical problems of the mathematical theory of hydrodynamic boundary layer”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 1, 11–20; Moscow University Mathematics Bulletin, 79:1 (2024), 11–21
2023
4.
K. A. Bekmaganbetov, A. A. Tolemis, V. V. Chepyzhov, G. A. Chechkin, “On attractors of Ginzburg–Landau equations in domain with locally periodic microstructure. Subcritical, critical and supercritical cases”, Dokl. RAN. Math. Inf. Proc. Upr., 513 (2023), 9–14; Dokl. Math., 108:2 (2023), 346–351
5.
K. A. Bekmaganbetov, A. M. Toleubai, G. A. Chechkin, “On asymptotics of attractors to Navier–Stockes system in anisotropic medium with small periodic obstacles”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 42–46; Dokl. Math., 108:1 (2023), 277–281
M. A. Kisatov, V. N. Samokhin, G. A. Chechkin, “О пограничном слое Марангони в вязкой неньютоновской среде”, Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 174–195
2022
7.
M. A. Kisatov, V. N. Samokhin, G. A. Chechkin, “Erratum to: On thermal boundary layer in a viscous non-Newtonian medium”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 486; Dokl. Math., 106:3 (2022), 486
8.
M. A. Kisatov, V. N. Samokhin, G. A. Chechkin, “On thermal boundary layer in a viscous non-Newtonian medium”, Dokl. RAN. Math. Inf. Proc. Upr., 502 (2022), 28–33; Dokl. Math., 105:1 (2022), 23–27
K. A. Bekmaganbetov, V. V. Chepyzhov, G. A. Chechkin, “Strong convergence of attractors of reaction-diffusion system with rapidly oscillating
terms in an orthotropic porous medium”, Izv. RAN. Ser. Mat., 86:6 (2022), 47–78; Izv. Math., 86:6 (2022), 1072–1101
K. A. Bekmaganbetov, A. M. Toleubai, G. A. Chechkin, “On attractors of 2D Navier–Stockes system in a medium with anisotropic variable viscosity and periodic obstacles”, Zap. Nauchn. Sem. POMI, 519 (2022), 10–34
2021
11.
K. A. Bekmaganbetov, V. V. Chepyzhov, G. A. Chechkin, “On attractors of reaction–diffusion equations in a porous orthotropic medium”, Dokl. RAN. Math. Inf. Proc. Upr., 498 (2021), 10–15; Dokl. Math., 103:3 (2021), 103–107
Yu. A. Alkhutov, G. A. Chechkin, “Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation”, Dokl. RAN. Math. Inf. Proc. Upr., 497 (2021), 3–6; Dokl. Math., 103:2 (2021), 69–71
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; Proc. Steklov Inst. Math., 310 (2020), 32–69
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; J. Math. Sci. (N. Y.), 244:2 (2020), 158–169
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; Izv. Math., 82:6 (2018), 1108–1135
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; J. Math. Sci. (N. Y.), 234:4 (2018), 485–496
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; J. Math. Sci. (N. Y.), 234:4 (2018), 407–422
2015
18.
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; Izv. Math., 79:3 (2015), 467–511
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; J. Math. Sci. (N. Y.), 210:2 (2015), 115–134
2013
20.
A. Yu. Linkevich, S. V. Spiridonov, G. A. Chechkin, “Homogenization of stratified dilatant fluid”, CMFD, 48 (2013), 75–83; Journal of Mathematical Sciences, 202:6 (2014), 849–858
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
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; J. Math. Sci. (N. Y.), 179:4 (2011), 557–577
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
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, no. 14, 27–36
2009
25.
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; Sb. Math., 200:3 (2009), 357–383
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; Comput. Math. Math. Phys., 46:1 (2006), 97–110
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; Izv. Math., 69:4 (2005), 805–846
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; Math. Notes, 76:6 (2004), 865–879
G. A. Chechkin, “Splitting of a multiple eigenvalue in a problem on concentrated masses”, Uspekhi Mat. Nauk, 59:4(358) (2004), 205–206; Russian Math. Surveys, 59:4 (2004), 790–791
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; Differ. Equ., 39:5 (2003), 681–693
2002
31.
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; Differ. Equ., 38:10 (2002), 1481–1487
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; Russian Math. Surveys, 57:6 (2002), 1240–1242
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; Proc. Steklov Inst. Math., 236 (2002), 334–340
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; Proc. Steklov Inst. Math., 236 (2002), 148–156
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; Sb. Math., 192:7 (2001), 933–949
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, no. 1, 14–19
A. Yu. Belyaev, G. A. Chechkin, “Averaging of operators with a fine-scaled structure of boundary conditions”, Mat. Zametki, 65:4 (1999), 496–510; Math. Notes, 65:4 (1999), 418–429
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; Siberian Math. J., 40:2 (1999), 229–244
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; Siberian Math. J., 39:4 (1998), 621–644
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; Sb. Math., 186:4 (1995), 511–525
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; Russian Math. Surveys, 48:6 (1993), 173–175
G. A. Chechkin, “Averaging of boundary value problems with a singular perturbation of the boundary conditions”, Mat. Sb., 184:6 (1993), 99–150; Russian Acad. Sci. Sb. Math., 79:1 (1994), 191–222
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Goritsky, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, A. A. Kon'kov, V. V. Palin, E. V. Radkevich, V. V. Rogachev, O. S. Rozanova, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, M. V. Shamolin, T. A. Shaposhnikova, “К 70-летию Валерия Васильевича Козлова”, Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 3–7
2011
44.
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; Journal of Mathematical Sciences, 190:1 (2013), 1–7
45.
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; J. Math. Sci. (N. Y.), 179:3 (2011), 345–346
2007
46.
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; J. Math. Sci. (N. Y.), 143:4 (2007), 3183–3197
2005
47.
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, no. 5, 77–79
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; Russian Math. Surveys, 58:1 (2003), 161–172
2000
49.
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; Russian Math. Surveys, 55:5 (2000), 977–985
The Boyarsky–Meyers Inequality for Elliptic Equations G. A. Chechkin VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 17, 2023 12:55
5.
Elliptic Equations and Meyers Estimates Yu. A. Alkhutov, G. A. Chechkin International Conference Dedicated to the 100th Anniversary of the Birthday
of V. S. Vladimirov (Vladimirov-100) January 10, 2023 18:00
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
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