@article{ZVMMF_2015_55_11_a4,
author = {A. B. Aliyev and S. E. Isayeva},
title = {A global attractor for one semilinear hyperbolic equation with memory operator},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1857--1869},
year = {2015},
volume = {55},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a4/}
}
TY - JOUR AU - A. B. Aliyev AU - S. E. Isayeva TI - A global attractor for one semilinear hyperbolic equation with memory operator JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2015 SP - 1857 EP - 1869 VL - 55 IS - 11 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a4/ LA - ru ID - ZVMMF_2015_55_11_a4 ER -
%0 Journal Article %A A. B. Aliyev %A S. E. Isayeva %T A global attractor for one semilinear hyperbolic equation with memory operator %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2015 %P 1857-1869 %V 55 %N 11 %U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a4/ %G ru %F ZVMMF_2015_55_11_a4
A. B. Aliyev; S. E. Isayeva. A global attractor for one semilinear hyperbolic equation with memory operator. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1857-1869. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a4/
[1] Kenmochi N., Visintin A., “Asymptotic stability for nonlinear evolution problems with hysteresis”, Europ. J. Appl. Math., 5 (1994), 39–56 | DOI | MR | Zbl
[2] Krejci P., “Hysterezis and periodic solutions of semilinear and quasilinear wave equations”, Math. Z., 193 (1986), 247–264 | DOI | MR | Zbl
[3] Krejci P., “Asymptotic stability of periodic solutions to the wave equation with hysteresis”, Models of hysteresis, ed. A. Visintin, Longman-Harlow, London, 1993, 77–90 | MR | Zbl
[4] Arosio A., Linear second order differential equations in Hilbert spaces. Existence, uniqueness and regularity of the solution to the Cauchy problem. Asymptotic behavior as $t\to\infty$, Inst. Mat. “Leonida Tonelli”, Univ. degli Studi di Pisa, February 1981
[5] Borzdyko V. I., “Uniqueness theorem for differential equations with hysteresis nonlinearities”, Differential Equat., 23 (1987), 623–626 | MR | Zbl
[6] Kopfova J., “Uniqeness theorem for a Cauchy problem with hysteresis”, Proc. American Math. Soc., 127:12 (1999), 3527–3532 | DOI | MR | Zbl
[7] Kopfova J., “Periodic solutions and asymptotic behavior of a PDE with hysteresis in the source term”, Rocky Mountain J. Math., 36:2 (2006), 539–554 | DOI | MR | Zbl
[8] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007
[9] Korpusov M. O., Sveshnikov A. G., “Ob odnoi nachalno-kraevoi zadache dlya silno nelineinogo dissipativnogo uravneniya sobolevskogo tipa”, Zh. vychisl. matem. i matem. fiz., 48:10 (2008), 1860–1877 | MR | Zbl
[10] Korpusov M. O., Sveshnikov A. G., “O razrushenii resheniya odnogo novogo statsionarnogo uravneniya sobolevskogo tipa”, Zh. vychisl. matem. i matem. fiz., 50:5 (2010), 876–893 | MR | Zbl
[11] Visintin A., “Hysteresis and semigroups”, Models of Hysteresis, ed. A. Visintin, Longman, Harlow, 1993, 192–206 | MR | Zbl
[12] Hilpert M., “On uniqueness for evolution problems with hysteresis”, Mathematical Models for Phase Change Problems, ed. J. F. Rodrigues, Birkhauser, Basel, 1989 | MR
[13] Lions Zh. L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972
[14] Visintin A., Differential models of hysteresis, Springer, New York, 1993 | MR
[15] Isayeva S. E., “The mixed problem for one semilinear hyperbolic equation with memory”, Transactions of NAS of Azerbaijan, XXX:1 (2010), 105–112 | MR | Zbl
[16] Ladyzhenskaya O. A., “O nakhozhdenii minimalnykh globalnykh attraktorakh dlya uravnenii Nave–Stoksa i drugikh uravnenii s chastnymi proizvodnymi”, UMN, 42:6 (2009), 25–60
[17] Isayeva S. E., “The existence of an absorbing set for one mixed problem with memory”, Transactions of NAS of Azerbaijan, XXXIII:1 (2013), 27–35
[18] Chueshov I., Lasiecka I., “Attractors for second'order evolution equations with a nonlinear damping”, J. Dynam. Differential Equations, 16:2 (2004), 469–512 | DOI | MR | Zbl
[19] Lasiecka I., Ruzmaikina A. R., “Finite dimensionality and regularity of attractors for 2'D semilinear wave equation with nonlinear dissipation”, J. Math. Anal. Appl., 270 (2002), 16–50 | DOI | MR | Zbl
[20] Khanmamedov A. Kh., “Global attractors for wave equations with nonlinear interior damping and critical exponents”, J. Differential Equations, 230 (2006), 702–719 | DOI | MR | Zbl