А.И. Комеч - Публикации

2015

Комеч А.И., Imaykin, Valeriy; Komech, Alexander; Spohn, Herbert; On the Lagrangian theory for rotating charge in the Maxwell field. Phys. Lett. A 379 (2015), no. 1-2, 5–10.

2014

Комеч А.И., On global attractors of Hamilton nonlinear PDEs, p. 59 in: Abstracts of The Seventh International Conference on Differential and Functional Differential Equations Moscow, Russia, August 22–29, 2014. http://dfde2014.mi.ras.ru/files/abstracts.pdf
Комеч А.И., On global attractors of Hamilton nonlinear PDEs, International conference "Stochastic and PDE Methods in Mathematical Physics", 15-17 September 2014, Paris, University of Paris-Diderot http://shirikyan.u-cergy.fr/detailed%20programme.pdf
Комеч А.И., Копылова Е.А., On eigenfunction expansion of solutions to the Hamilton equations, J. Stat. Phys. 154 (2014), no. 1-2, 503-521. arXiv:1308.0485. Co-authored by E. Kopylova. DOI 10.1007/s10955-013-0846-1

2013

Комеч А.И., A variant of the Titchmarsh convolution theorem for distributions on the circle, Funktsional. Anal. i Prilozhen. 47 (2013), no. 1, 26–32. [Russian] ; English translation in Funct. Anal. Appl. 47 (2013), no. 1, 21-26. Co-authored by A.A. Komech.
Комеч А.И., Копылова Е.А., 5th St.Petersburg Conference in Spectral Theory dedicated to the memory of M.Sh. Birman, July 2-6, 2013, Euler Institute, Saint-Petersburg, Russia. Title: On spectral resolution and eigenfunction expansions for Hamilton operators. http://www.pdmi.ras.ru/EIMI/2013/ST5/programme.pdf
Комеч А.И., Копылова Е.А., Копылов С., Nonlinear wave equations with parabolic potentials, Journal of Spectral Theory 3 (2013), 1-19. ArXiv 1206.6073.
Комеч А.А., Комеч А.И., On the Titchmarsh convolution theorem for distributions on a circle. Journal of Functional Analysis and Its Applications, 47 (2013), 21--26 DOI:10.1007/s10688-013-0003-2 http://arxiv.org/abs/1108.2463 http://dx.doi.org/10.1007/s10688-013-0003-2
Комеч А.И., Quantum Mechanics: Genesis and Achievements, Springer, Dordrecht, 2012. 285 pages. ISBN 978-94-007-5542-0 http://www.springer.com/physics/quantum+physics/book/978-94-007-5541-3
Комеч А.И., Мерзон А., On asymptotic completeness of scattering in the nonlinear Lamb system II, J. Math. Physics 54(2013), 012702-012710. arXiv:1205.5850 http://dx.doi.org/10.1063/1.4773288
Комеч А.И., Копылова Е., Карлович Ю., Мерзон А., On the spreading rate of the soliton perturbation for relativistic nonlinear wave equation, accepted in Comm. Math. Analysis 14 (2013), no. 2, 95-102. Co-authored by E. Kopylova, Yu. Karlovich, A.Merzon.
Комеч А.И., Копылова Е., Weighted decay for magnetic Schrdinger equation, J. Funct. Analysis 264 (2013), no. 3, 735-751. http://dx.doi.org/10.1016/j.jfa.2012.12.001

2012

Комеч А.И., Копылова Е., Dispersive estimates for magnetic Schrodinger and Klein-Gordon equations, 6th European Congress of Mathematics, Krakow, July 2-7, 2012. http://www.6ecm.pl/en/programme/posters
Комеч А.И., Копылова Е., Dispersive estimates for magnetic Schroedinger and Klein-Gordon equations, p. 210 in: Abstracts of International Conference on Differential Equations and Dynamical Systems, Suzdal, June 29-July 4, 2012.
Комеч А.И., On global attractors of nonlinear hyperbolic PDEs, p. 27 in: DIFFERENTIAL EQUATIONS AND APPLICATIONS, International Conference in Honour of Mark Vishik On the occasion of his 90th birthday, Moscow, June 4-7, 2012. http://www.dynamics.iitp.ru/vishik/abstracts/abstracts.pdf
Комеч А.И., Global attractors of nonlinear hyperbolic PDEs, Abstracts, International Workshop ”Analysis, Operator Theory, and Mathematical Physics”. January 23 - 27, 2012, Ixtapa, Mexico. http://www.lsis.org/gauthierjp/mexique/ixtapa.pdf
Комеч А.И., Копылова Е., Dispersion Decay and Scattering Theory, John Wiley & Sons, Hoboken, NJ, 2012. 202 pages. ISBN 978-1-118-34182-7 http://www.wiley-vch.de/publish/en/books/ISBN978-1-118-34182-7
Комеч А.И., Копылова Е., Копылов C., On nonlinear wave equations with parabolic potentials, arXiv:1206.6073. Co-authored by Elena Kopylova, Sergey Kopylov
Комеч А.И., On wave theory of the photoeffect, arXiv:1206.3680.
Комеч А.И., On Dynamical Justification of Quantum Scattering Cross Section, arXiv:1206.3677.
Комеч А.И., Имайкин В., Шпон Г., On Lagrangian Theory for Rotating Charge Coupled to the Maxwell Field, arXiv:1206.3641.
Комеч А.И., Мерзон А., On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II, arXiv:1205.5850
Комеч А.И., Копылова Е., Weighted decay for magnetic Schroedinger equation. arXiv:1204.1731.
Комеч А.И., Копылова Е., On convergence to equilibrium distribution for Dirac equation, arXiv:1201.6221.
Комеч А.И., Имайкин В., Вайнберг Б., Scattering of solitons for coupled wave-particle equations, J. Math. Analysis and Appl. 389 (2012), no. 2, 713-740. arXiv:1006.2618 http://dx.doi.org/10.1016/j.jmaa.2011.12.016
Комеч А.И., Копылова Е., Стюарт Д., On asymptotic stability of solitary waves for Sch¨odinger equation coupled to nonlinear oscillator, II. Comm. Pure Appl. Anal. 11 (2012), no. 3, 1063-1079. doi:10.3934/cpaa.2012.11.1063

2011

Комеч А.И., Шпон Г., Имайкин В., Scattering asymptotics for a charged particle coupled to the Maxwell field, J. Math. Physics 52 (2011), no. 4, 042701-1–042701-33. arXiv:0807.1972 http://dx.doi.org/10.1063/1.3567957
Комеч А.И., Копылова Е., On convergence to equilibrium distribution for Dirac equation, Markov processes and related fields 17 (2011), 523-540.
Комеч А.И., Копылова Е., On asymptotic stability of kink for relativistic Ginzburg-Landau equation, Arch. Rat. Mech. Anal. 202 (2011), no. 2, 213-245. ArXiv:0910.5539 DOI: 10.1007/s00205-011-0415-1
Комеч А.И., Копылова Е., Шпон Г., Scattering of solitons for Dirac equation coupled to a particle, J. Math. Analysis and Appl. 383 (2011), no. 2, 265-290. arXiv:1012.3109 http://dx.doi.org/10.1016/j.jmaa.2011.05.037
Комеч А.И., Копылова Е., On asymptotic stability of moving kink for relativistic Ginzburg-Landau equation, Comm. Math. Physics 302 (2011), no. 1, 225-252. ArXiv:0910.5538 DOI: 10.1007/s00220-010-1184-7
Комеч А.И., Комеч А.А., On global attraction to quantum stationary states. Dirac equation with mean field interaction. Commun. Math. Anal. (2011), Conference 3, 131--136. http://arXiv.org/abs/0910.0517 http://math-res-pub.org/cma/proceedings/74-conference-3-cma
Комеч А.А., Комеч А.И., Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time, Russian Journal of Mathematical Physics 18 (2011), no. 4, 410--419. DOI:10.1134/S1061920811040030 http://arxiv.org/abs/1008.3032 http://dx.doi.org/10.1134/S1061920811040030

2010

Комеч А.А., Комеч А.И., Global attraction to solitary waves for nonlinear Dirac equation with mean field interaction, SIAM J. Math. Anal. 42 (2010), no. 6, 2944--2964. DOI:10.1137/090772125 http://dx.doi.org/10.1137/090772125
Комеч А.И., Комеч А.А., Global attractor for the Klein-Gordon field coupled to several nonlinear oscillators, Journal de Mathématiques Pures et Appliquées 93 (2010), no. 1, 91--111. DOI:10.1016/j.matpur.2009.08.011 http://arxiv.org/abs/math.AP/0702660 http://dx.doi.org/10.1016/j.matpur.2009.08.011
Копылова Е.А., Комеч А.И., Weigted energy decay for 3D Klein-Gordon equation, Journal of Diff.Equations, 248 (2010), n.3, p.501-520.

2009

Комеч А.И., Комеч А.А., Global attraction to solitary waves for Klein-Gordon equation with mean field interaction. Annales de l"Institute Henri Poincaré (Analyse non linéaire) 26 (2009), no. 3, 855--868 DOI:10.1016/j.anihpc.2008.03.005 http://arxiv.org/abs/0708.1131 http://dx.doi.org/10.1016/j.anihpc.2008.03.005
Комеч А.И., Комеч А.А., Principles of Partial Differential Equations, Springer, 2009. ISBN 978-1-4419-1095-0 DOI:10.2007/978-1-4419-1096-7 http://dx.doi.org/10.2007/978-1-4419-1096-7
Комеч А.И., Weighted energy decay for 1D Klein-Gordon equation, accepted in Comm. PDE, 2009. Co-authored by E. Kopylova.
Комеч А.И., Weighted energy decay for 3D Klein-Gordon equation, accepted in J. Differential Equations, 2009. Co-authored by E. Kopylova.
Комеч А.И., On global attraction to solitary waves for the Klein-Gordon field coupled to several nonlinear oscillators, accepted in J. des Mathematiques Pures et App., 2009. Co-authored by A. Comech. arXiv:math/0702660
Комеч А.И., Global attraction to solitary waves for Klein-Gordon equation with mean field interaction, Annales de l"IHP-ANL 26 (2009), no. 3, 855-868. Co-authored by A.A. Komech. arXiv:math-ph/0711.1131
Комеч А.И., On asymptotic completeness of scattering in the nonlinear Lamb system, J. Math. Physics 50 (2009), 023514-1 -- 023514-10. Co-authored by A.E. Merzon
Комеч А.И., Scattering in the nonlinear Lamb system, Physics Letters A 373 (2009), 1005-1010. Co-authored by A.E. Merzon

2008

Комеч А.И., Комеч А.А., Global attraction to solitary waves in models based on the Klein-Gordon equation. SIGMA 4 (2008), 010. 1--23. Proceedings of the Seventh International Conference ``Symmetry in Nonlinear Mathematical Physics" (June 24-30, 2007; Institute of Mathematics, Kyiv, Ukraine). DOI:10.3842/SIGMA.2008.010 http://arxiv.org/abs/0711.0041 http://dx.doi.org/10.3842/SIGMA.2008.010
Комеч А.И., On asymptotic stability of solitary waves in nonlinear Schr"odinger equation, Comm. Partial Diff. Eqns 33 (2008), no. 4, 669-705. arXiv:math-ph/0702013 Co-authored by V. Buslaev, E. Kopylova and D. Stuart.
Комеч А.И., On dispersive properties of discrete 2D Schr"odinger and Klein-Gordon equations, J. Funct. Analysis 254 (2008), no. 8, 2227-2254.Co-authored by E. Kopylova and B. Vainberg. Co-authored by E. Kopylova and B. Vainberg.

2007

Комеч А.И., Комеч А.А., Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field. Arch. Ration. Mech. Anal. 185 (2007), no. 1, 105--142 DOI:10.1007/s00205-006-0039-z http://arxiv.org/abs/math.AP/0609013 http://dx.doi.org/10.1007/s00205-006-0039-z
Комеч А.И., Комеч А.А., Global well-posedness for the Schrodinger equation coupled to a nonlinear oscillator. Russ. J. Math. Phys. 14 (2007), no. 2, 164--173 DOI:10.1134/S1061920807020057 http://arxiv.org/abs/math.AP/0608780 http://dx.doi.org/10.1134/S1061920807020057
Комеч А.И., On relation between the Cauchy data in scattering by wedge, Russ. J. Math. Phys. 14 (2007), no. 3, 279-303.Co-authored by A.E. Merzon.
Комеч А.И., Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field, Arch. Rat. Mech. Anal. 185 (2007), 105-142.Co-authored by A.A. Komech.

2006

Комеч А.И., Dispersive estimates for 1D discrete Schr"odinger and Klein-Gordon equations, Applicable Analysis 85 (2006), no. 12, 1487-1508. Co-authored by E. Kopylova and M. Kunze.
Комеч А.И., On scattering of solitons for the Klein-Gordon equation coupled to a particle, Comm. Math. Phys. 268 (2006), no. 2, 321-367. arXiv:math.AP/0609205 Co-authored by V. Imaikin and B. Vainberg.
Комеч А.И., Комеч А.А., On global attraction to solitary waves for the Klein-Gordon equation coupled to nonlinear oscillator, C. R., Math., Acad. Sci. Paris 343, Issue 2, 15 July 2006, Pages 111--114. DOI:10.1016/j.crma.2006.06.009 http://iitp.ru/ http://dx.doi.org/10.1016/j.crma.2006.06.009
Комеч А.И., On metastable regimes in stochastic Lamb system, Journal of Mathematical Physics 47 (2006), no. 4, 043301-1 -- 043301-12. Co-authored by M. Freidlin.
Комеч А.И., Limiting amplitude principle in the diffraction by wedges, Mathematical Methods in Applied Sciences 29 (2006), no. 10, 1147-1185.Co-authored by A.E. Merzon.
Комеч А.И., Scattering of solitons for Schr"odinger equation coupled to a particle, Russian J. Math. Phys. 13 (2006), no. 2, 158-187. arXiv:math.AP/0609649 Co-authored by E.A. Kopylova.
Комеч А.И., On two-temperature problem for the Klein-Gordon equation, Theory Prob. Appl. 50 (2006), no. 4, 582-611.Co-authored by T. Dudnikova.

2005

Комеч А.И., Двух-температурная задача для уравнения Клейна-Гордона, Теория Вероятностей и ее Приложения, 50 (2005), № 4, 675-710. Co-authored by T. Dudnikova.
Комеч А.И., On convergence to equilibrium distribution for Schr"odinger equation, Markov Processes and Related Fields, 11 (2005), no. 1, 81-110. Co-authored by E. Kopylova and N. Mauser.
Комеч А.И., On the convergence to a statistical equilibrium in the crystal coupled to a scalar field, Russ. J. Math. Phys. 12 (2005), no. 3, 301-325. Co-authored by T. Dudnikova.
Комеч А.И., On Sommerfeld representation and uniqueness in diffraction by wedges, Mathematical Methods in Applied Sciences 28 (2005), no. 2, 147-183. Co-authored by N.J. Mauser and A.E. Merzon.

2004

Комеч А.И., On attraction to solitons in relativistic nonlinear wave equations, Russ. J. Math. Phys. 11 (2004), no. 3, 289-307. Co-authored by N. Mauser and A. Vinnichenko.
Комеч А.И., Soliton-type asymptotics for the coupled Maxwell-Lorentz equations, Ann. Inst. Poincar"e, Phys. Theor. 5 (2004), 1117-1135. Co-authored by V. Imaikin and N. Mauser.
Комеч А.И., Rotating charge coupled to the Maxwell field: scattering theory and adiabatic limit, Monatshefte fuer Mathematik 142 (2004), no. 1-2, 143-156. Co-authored by V. Imaikin and H. Spohn.
Комеч А.И., On convergence to equilibrium distribution for wave equation in even dimensions, Ergodic Theory and Dynamical Systems 24 (2004), 1-30. Co-authored by E. Kopylova and N. Mauser.
Комеч А.И., On two-temperature problem for harmonic crystals, Journal of Statistical Physics 114 (2004), no. 3/4, 1035-1083. Co-authored by T. Dudnikova and N. Mauser.
Комеч А.И., Scattering theory for a particle coupled to a scalar field, Journal of Discrete and Continuous Dynamical Systems 10 (2004), no. 12, 387-396. Co-authored by V. Imaikin and H. Spohn.

2003

Комеч А.И., On the convergence to a statistical equilibrium for the Dirac equation, Russian Journal of Math. Phys. 10 (2003), no. 4, 399-410. Co-authored by T. Dudnikova and N. Mauser.
Комеч А.И., On convergence to statistical equilibrium for harmonic crystals, Journal of Mathematical Physics 44 (2003), no. 6, 2596-2620. Co-authored by T. Dudnikova and H. Spohn.
Комеч А.И., Scattering of solitons of the Klein-Gordon equation coupled to a classical particle, Journal of Mathematical Physics 44 (2003), no. 3, 1202-1217. Co-authored by V. Imaikin and P. Markowich.

2002

Комеч А.И., Breathers for a relativistic nonlinear wave equation, Arch. Rat. Mech. Anal. 165 (2002), 317-345. Co-authored by A. Bensoussan and C. Iliine.
Комеч А.И., Soliton-like asymptotics and scattering for a particle coupled to Maxwell field, Russian Journal of Mathematical Physics 9 (2002), no. 4, 428-436. Co-authored by V. Imaikin and H. Spohn.
Комеч А.И., Energy-momentum relation for solitary waves of relativistic wave equation, Russian Journal Math. Phys. 9 (2002), no. 2, 153-160. Co-authored by T. Dudnikova and H. Spohn.
Комеч А.И., A method of complex characteristics for elliptic problems in angles and its applications, pp 125-159 in: Translations. Series 2. American Mathematical Society. 206, American Mathematical Society (AMS), Providence, RI, 2002. Co-authored by A. Merzon and P. Zhevandrov.
Комеч А.И., On a two-temperature problem for wave equation with mixing, Markov Processes and Related Fields 8 (2002), no. 1, 43-80. Co-authored by T.~Dudnikova and H.~Spohn.
Комеч А.И., On convergence to equilibrium distribution, II. Wave equation with mixing, Journal of Statistical Physics 108} (2002), no. 4, 1219-1253. Co-authored by T.V.~Dudnikova, N.E.~Ratanov and Yu.M.~Suhov.
Комеч А.И., On convergence to equilibrium distribution, I. Klein-Gordon equation with mixing, Comm. Math. Phys. 225 (2002), no. 1, 1-32. Co-authored by T.V.~Dudnikova, E.A.~Kopylova and Yu.M.~Suhov.

2001

Комеч А.И., On a stabilization of the string interaction with two nonlinear oscillators, Moscow Univ. Math. Bull.} 56 (2001), no. 3, 3-10. Co-authored by Yu.E.~Egorov.

2000

Комеч А.И., Attractors of non-linear Hamiltonian one-dimensional wave equations, Russ. Math. Surv. 55 (2000), no. 1, 43-92.
Комеч А.И., Long-time asymptotics for the coupled Maxwell-Lorentz equations, Comm. Partial Diff. Eqns. 25 (2000), no. 3/4, 558-585. Co-authored by H.~Spohn.

1988

Комеч А.И., Вишик М.И., Periodic approximations of homogeneous measures. In: Mathematical problems of statistical hydromechanics.— Kluver Academic Publishers, Dordrecht, Boston, London, 1988, p. 534—562.

1985

Вишик М.И., Комеч А.И., Об оценке среднего квадрата разности скоростей для однородных статистических решений трехмерной системы Навье-Стокса. Труды сем. им. И.Г.Петровского, 1985, 11, с. 3—11.

1984

Вишик М.И., Комеч А.И., Задача Коши для уравнения Хопфа, Лиувилля и прямого и обратного уравнений Колмогорова. В сб.: Н.Е. Кочин и развитие механики.— Москва: Наука, 1984, с. 202—218.

1983

Вишик М.И., Комеч А.И., Об уравнениях Колмогорова, соответствующих двумерной стохастической системе Навье-Стокса. Труды ММО, 1983, 46, с. 3—43.

1982

Вишик М.И., Комеч А.И., Сильные решения двумерной стохастической системы Навье-Стокса и со ответствующие уравнения Колмогорова.— Zeitschrift fur Analysis und ihre Anwendungen, 1982, 1:3, s. 23—52 (совм. с А.И.Комечем).
Вишик М.И., Комеч А.И., Статистические решения системы Навье-Стокса и системы Эйлера. Успехи механики, 1982, 5:1 (2), с. 65—120.
Вишик М.И., Комеч А.И., Обобщенные решения обратного уравнения Колмогорова, соответствующего стохастической системе Навье-Стокса. Труды сем. им. И.Г.Петровского, 1982, 8, с. 86—110.

1981

Вишик М.И., Комеч А.И., Индивидуальные и статистические решения двумерной системы Эйлера. ДАН СССР, 1981, 261:4, с. 780—785.
Вишик М.И., Комеч А.И., О стохастической системе Навье-Стокса и соответствующих уравнениях Колмогорова. ДАН СССР, 1981, 257:6, с. 1298—1301.
Вишик М.И., Комеч А.И., Слабые решения обратного уравнения Колмогорова, соответствующего статистической системе Навье-Стокса. УМН, 1981, 36:3(219), с. 205—206. http://mi.mathnet.ru/umn2932
Вишик М.И., Комеч А.И., Прямое и обратное уравнения Колмогорова, соответствующие стохастической системе Навье- Стокса. Совместные заседания семинара имени И. Г. Петровского по дифференциальным уравнениям и математическим проблемам физики и Московского математического общества. УМН, 1981, 36:4(220), с. 236. http://mi.mathnet.ru/umn3012

1980

Вишик М.И., Комеч А.И., Stationary solutions of the stochastic Navier — Stokes equations. In: Lecture Notes in Control and Information Sciences.— Springer, 1980, p. 103—113 .
Вишик М.И., Комеч А.И., Однородные по х решения стохастической системы Навье-Стокса с белым шумом. В кн.: Математические задачи статистической гидромеханики, Дополнение II, М.: Наука, 1980, с. 350— 429.
Вишик М.И., Комеч А.И., Об однозначной разрешимости задачи Коши для прямого уравнения Колмогорова, соответствующего двумерной стохастической системе Навье-Стокса. Совместные заседания семинара имени И. Г. Петровского по дифференциальным уравнениям и математическим проблемам физики и Московского математического общества (третья сессия, 8–10 января 1980 г.). УМН, 1980, 35:4 (214), с. 163—164. http://mi.mathnet.ru/umn3657

1979

Вишик М.И., Комеч А.И., Трансляционно однородные решения стохастической системы Навье-Стокса. ДАН, 1979, 246:5, с. 1037—1041.
Вишик М.И., Комеч А.И., Фурсиков А.В., Некоторые математические задачи статистической гидромеханики. УМН, 1979, 34:5 (209), с. 135—210. http://mi.mathnet.ru/umn4122

1978

Вишик М.И., Комеч А.И., Фурсиков А.В., Однородные по х пространственно-временные статистические решения и индивидуальные решения с неограниченной энергией системы Навье-Стокса. Совместные заседания семинара имени И. Г. Петровского по дифференциальным уравнениям и математическим проблемам физики и Московского математического общества (18–20 января 1978 г.). УМН, 1978, 33:3 (201), с. 133—134. http://mi.mathnet.ru/umn3425
Вишик М.И., Комеч А.И., О разрешимости задачи Коши для прямого уравнения Колмогорова, соответствующего стохастическому уравнению типа Навье — Стокса. В кн.: Комплексный анализ и его приложения.— М.: Наука, 1978, с. 126—136.
Вишик М.И., Комеч А.И., О задаче Коши для бесконечномерных параболических дифференциальных уравнений второго порядка. Труды сем. им. И. Г. Петровского, 1978, 4, с. 3—31.
Вишик М.И., Комеч А.И., О разрешимости задачи Коши для уравнения Хопфа, соответствующего нелинейному гиперболическому уравнению. Труды сем. им. И. Г. Петровского, 1978, 3, с. 19—42.
Вишик М.И., Комеч А.И., Фурсиков А.В., Homogeneous stochastic solutions of the Navier-Stokes equations, In: International Symposium on stochastic differential equations. Vilnius, 1978, p. 114—117.

1977

Вишик М.И., Комеч А.И., О прямом уравнении Колмогорова, соответствующем стохастическим параболическим уравнениям и системе Навье-Стокса. Вторая Вильнюсская конференция по теории вероятностей и математической статистике, Вильнюс, 1977, с.80—81.
Вишик М.И., Комеч А.И., Бесконечномерные параболические уравнения, связанные со стохастическими уравнениями в частных производных. ДАН, 1977, 233:5, с. 769—772.