Monographs
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A. Komech, E. Kopylova,
Dispersion Decay and Scattering Theory,
John Wiley & Sons, Hoboken, NJ, 2012.
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A. Komech, E. Kopylova,
Attractors of Hamilton Nonlinear Partial Differential Equations,
Cambridge University Press, Cambridge, 2021.
Papers
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A. Komech, E. Kopylova,
On the Hamilton--Poisson structure and solitons for the Maxwell--Lorentz equations with spinning particle
.
J. Math. Anal. Appl .
522 (2023), no. 2, 126976.
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A. Komech, E. Kopylova,
On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle
.
Milan Journal of Mathematics .
(2023).
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E. Kopylova, G. Teschl,
Scattering properties and dispersion estimates for one dimensional discrete Dirac equation
.
Mathematische Nachrichten .
295 (2022), no. 44, 762-784.
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A. Komech, E. Kopylova,
On global attractors for 2D damped driven nonlinear Schrödinger equations
.
Applicable Analysis .
101 (2022), no. 15, 5490-5503.
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E. Kopylova,
Global attractor for 3D Dirac equation with nonlinear point interaction
.
Nonlinear Differential Equations and Applications NoDEA .
29 (2022), no. 3, 1-44.
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E. Kopylova,
Klein-Gordon equation with mean field interaction.
Orbital and asymptotic stability of solitary waves
.
Nonlinearity .
35 (2022), no. 7, 3593-3629.
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E. Kopylova,
On dispersive estimates for one-dimensional Klein-Gordon equations
.
Asympt. Analysis .
127 (2022), 1-13.
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A. Comech, E. Kopylova,
On spectral and orbital stability for the Klein-Gordon equation coupled to an anharmonic oscillator
.
Comm. Pure Appl. Anal .
20 (2021), no. 6, 2187-2209.
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A. Komech, E. Kopylova,
Attractors of Hamilton nonlinear partial differential equations
.
Russian Math. Surveys .
75 (2020), no. 1, 1-87.
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E. Kopylova, A. Komech,
Global attractor for 1D Dirac field coupled to nonlinear oscillator
.
Comm. Math. Physics .
375 (2020), no. 2, 573-603.
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E. Kopylova, A. Komech,
On global attractor of 3D Klein-Gordon with several concentrated nonlinearities
.
Dynamics of PDEs .
16 (2019), no. 2, 105-124.
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A. Komech, E. Kopylova,
On the dispersion decay for crystals in the linearized Schrödinger-Poisson model
.
J. Math. Anal. Appl .
50 (2018), no. 1, 864-882.
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E. Kopylova,
On Dispersion decay for 3D Klein-Gordon equation
.
Discrete and Continuous Dynamical System .
38 (2018), no. 11, 5765-5780.
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A. Komech, E. Kopylova,
On orbital stability of ground states for finite crystals in fermionic Schrödinger-Poisson model
.
SIAM J. Math. Anal .
50 (2018), no. 1, 64-85.
ArXiv 1711.02938
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E. Kopylova,
On global attraction to stationary states for wave equations with concentrated nonlinearities
.
J. Dynamics and Differential Equations .
30 (2018), no. 1, 107-116.
ArXiv 1611.04463
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A. Komech, E. Kopylova, H. Spohn,
On global attractors and radiation damping for nonrelativistic particle coupled to scalar field
.
St. Petersburg Math. J .
29 (2018), no. 2, 249-266.
ArXiv 1611.03272
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E. Kopylova,
On global attraction to solitary waves for the Klein -Gordon equation with concentrated nonlinearity
.
Nonlinearity .
30 (2017), 4191-4207.
ArXiv 1611.09882
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A. Komech, E. Kopylova,
On stability of ground states for finite crystals in the Schrödinger-Poisson model
.
J. Math. Phys .
58 (2017), no. 3, 031902.
ArXiv 1511.07074
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E. Kopylova,
On global well-posedness for Klein-Gordon equation with concentrated
nonlinearity
.
J. Math. Anal. Appl. .
443 (2016), no. 2, 1142-1157.
ArXiv 1607.00377
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A. Komech, E. Kopylova,
On linear stability of crystals in the Schrödinger-Poisson model
.
J. Stat. Phys .
165 (2016), no. 2, 246-273.
ArXiv 1505.07074
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A. Komech, E. Kopylova,
Asymptotic stability of stationary states in wave equation coupled to nonrelativistic particle
,
Russ. J. Math. Phys.
23 (2016), no. 1, 93-100.
ArXiv 1511.08680
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I. Egorova, E. Kopylova, V. Marchenko, G. Teschl,
Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited
,
Russian Math. Surveys .
71 (2016), no. 3, 391-415.
ArXiv 1411.0021
- E. Kopylova, G. Teschl,
Dispersion estimates for one-dimensional discrete Dirac equations
,
J. Math. Anal. Appl. .
434 (2016), no. 1, 191-208.
ArXiv 1507.02126
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I. Egorova, E. Kopylova, G. Teschl,
Dispersion estimates for one-dimensional discrete Schrödinger
and wave equations
,
Journal of Spectral Theory .
5 (2015), no. 4, 663-696.
ArXiv 1403.7803
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E. Kopylova,
Limiting absorption principle for the 1D discrete Dirac equation
,
Russ. J. Math. Phys. .
22 (2015), no. 1, 34-38.
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A. Komech, E. Kopylova,
Weighted energy decay for magnetic Klein-Gordon equations
,
Applicable Analysis .
94 (2015), no. 2, 219-233.
ArXiv 1308.0485
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A. Komech, E. Kopylova,
On the eigenfunction expansion for the Hamilton operators
,
Journal of Spectral Theory .
5 (2015), no. 2, 331-361.
ArXiv 1405.4122
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A. Komech, E. Kopylova,
On eigenfunction expansion of solutions to the Hamilton equations
,
Journal of Statistical Physics . 154 (2014), no. 1-2, 503-521.
ArXiv 1308.0485
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E. Kopylova,
Dispersion estimates for 2D Dirac equation
,
Asymptotic Analysis , 84 (2013), 35-46.
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E. Kopylova,
Asymptotic stability of solitons for nonlinear hyperbolic equations
,
Russian Math. Surveys , 68 (2013), no. 2, 283-334.
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A.I. Komech, E. Kopylova, S. Kopylov,
Nonlinear wave equations with parabolic potentials
,
J. Spectral Theory , 3 (2013), 1-19.
ArXiv 1206.6073.
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A.I. Komech, E. Kopylova,
Dispersion decay for magnetic Schrödinger equation
,
J. Funct. Analysis 264 (2013), 735-751.
ArXiv 1204.1731.
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E. Kopylova, A. Komech, Y. Karlovich, A. Merzon,
On the spreading rate of the soliton perturbation for relativistic nonlinear wave equation
,
Comm. Math. Analysis 14 (2013), no. 2, 95-102.
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A.I. Komech, E. Kopylova, D. Stuart,
On asymptotic stability of solitary waves for Schrödinger
equation coupled to nonlinear oscillator, II,
Comm. Pure Appl. Anal. 202 (2012),
no. 3, 1063-1079. ArXiv 0807.1878.
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E. Kopylova,
On long time decay for magnetic
Schrödinger and Klein-Gordon equations
,
Proceedings of the Steklov Institute of Mathematics , 278 (2012), 121-129.
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A.I. Komech, E.A. Kopylova, H. Spohn,
Scattering of solitons for Dirac equation
coupled to a particle ,
J. Math. Analysis and Appl. 383 (2011),
no. 2, 265-290. ArXiv 1012.3109.
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A.I. Komech, E.A. Kopylova,
On convergence to equilibrium distribution for Dirac
equation
, Markov Processes Related Fields 17 (2011), no. 4, 523-540.
ArXiv 1201.6221.
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E.A. Kopylova, A.I. Komech,
On asymptotic stability of kink for relativistic
Ginzburg-Landau equation
, Arch. Rat. Mech. Anal. 202 (2011), no. 2, 213-245.
ArXiv 0910.5539.
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E. Kopylova,
Weighted energy decay for modified
Klein-Gordon equation,
Comm. Math. Analysis, Conference 03
(2011), 137-152.
ArXiv 1009.2649.
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E. Kopylova,
Weighted energy decay for 1D Dirac
equation,
Dynamics of PDE
8 (2011), no. 2, 113-125.
ArXiv 1102.2157.
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E.A. Kopylova, A.I. Komech,
On asymptotic stability of moving kink for relativistic
Ginzburg-Landau equation ,
Comm. Math. Physics, 302 (2011), no.1, 225-252.
ArXiv 0910.5538.
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A.I. Komech, E. Kopylova,
Long time decay for
2D Klein-Gordon equation,
J. Functional Analysis
259 (2010), no. 2, 477-502.
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E. Kopylova,
Dispersion estimates for Schrödinger and Klein-Gordon equation
,
Russian Math. Survey
65 (2010), no. 1, 95-142.
http://iopscience.iop.org/0036-0279/65/1/R02/pdf/0036-0279_65_1_R02.pdf
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A.I. Komech, E. Kopylova,
Weighted energy decay for
1D Klein-Gordon equation,
Comm. PDE
35 (2010), 353-374.
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E. Kopylova,
Dispersion estimates for the 2D
wave equation,
Russian J. Math. Phys.
17 (2010), no. 2, 226-239.
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E. Kopylova,
Weighted energy decay for 1D wave equation
,
J. Math. Anal. Appl
366 (2010), no. 2, 494-505.
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A.I. Komech, E. Kopylova,
Weighted energy decay for
3D Klein-Gordon equation,
J. Differential Equations
248 (2010), no. 3, 501-520.
ArXiv 1003.3799.
doi:10.1016/j.jde.2009.06.011
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E. Kopylova,
On dispersion estimates for discrete 3D Schrödinger and Klein-Gordon equation
,
St. Peretersburg Math. J.
21 (2010), 743-760.
ArXiv 0812.0468.
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E. Kopylova,
On asymptotic stability of solitary waves in discrete Klein-Gordon equation
coupled to nonlinear oscillator
,
Applicable Analysis
89 (2010), no. 9, 1467-1493.
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E. Kopylova,
On decay of the Schrödinger resolvent
,
Proceedings of the Steklov Institute of Mathematics
270 (2010), 165-171.
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E. Kopylova,
On asymptotic stability of solitary waves in discrete Schrödinger equation
coupled to a nonlinear oscillator
,
Nonlinear Analysis Series A: Theory, Methods and Applications
71 (2009), no. 7-8, 3031-3046.
ArXiv 0805.3403.
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E. Kopylova,
Weighted energy decay for 3D wave equation
,
Asymptotic Analysis
65 (2009), no. 1-2, 1-16.
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V. Buslaev, A. Komech, E. Kopylova, D. Stuart,
On asymptotic
stability of solitary waves in nonlinear Schrödinger equation,
Comm. Partial Diff. Eqns
33 (2008), no. 4, 669-705. ArXiv math-ph/0702013.
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E. Kopylova,
Existence of solitary waves for the discrete Schrödinger equation
coupled to a nonlinear oscillator
,
Russian J. Math. Phys.
15 (2008), no. 4, 486-491.
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A. Komech, E. Kopylova, B. Vainberg,
On dispersion properties of discrete 2D
Schr\"odinger and Klein-Gordon equations
,
J. Funct. Anal.
254 (2008), no. 8, 2227-2254.
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A. Komech, E. Kopylova, M. Kunze,
Dispersion estimates for 1D discrete
Schrödinger and Klein-Gordon equations,
Applicable Analysis
85 (2006), no. 12, 1487-1508.
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A. Komech, E.A. Kopylova,
Scattering of solitons
for Schrödinger equation coupled to a particle,
Russian J. Math. Phys. 50 (2006),
no. 2, 158-187. arXiv:math/0609649.
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A. Komech, E.Kopylova, N.Mauser,
On convergence
to equilibrium distribution for Schrödinger equation,
Markov Processes and Related Fields
11 (2005),
no. 1, 81-110.
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A. Komech, E.Kopylova, N.Mauser,
On convergence to
equilibrium distribution for wave equation
in even dimensions,
Ergodic Theory and Dynamical Systems
24 (2004), 1-30.
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T.V. Dudnikova, A.I. Komech, E.A. Kopylova, Yu.M. Suhov,
On convergence to equilibrium
distribution, I. Klein-Gordon equation with mixing,
Comm. Math. Phys.
225 (2002), no. 1, 1-32. ArXiv math-ph/0508042.
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E.Kopylova,
Stabilization of statistical solutions of the Klein-Gordon equation
,
Mosc. Univ. Math. Bull. 41 (1986), no. 2, 72-75.
http://www.zentralblatt-math.org/zbmath/?index_=1979261&type_=pdf
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E.Kopylova,
Stabilization of the moment functions of the statistical solution of the wave equation
,
Mosc. Univ. Math. Bull. 40 (1985), 65-69.
http://www.zentralblatt-math.org/zbmath/?index_=2010433&type_=pdf
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E.Kopylova,
On stabilization of statistical solutions of the Klein-Gordon equation
,
Russian Math. Survey 40 (1985), no. 5 (245), 240-241 [Russian].
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=2767&option_lang=rus