Uniform attractors for vanishing viscosity approximations of non-autonomous complex flows

Nataliia V. Gorban, Oleksiy V. Kapustyan, Pavlo O. Kasyanov, Olha V. Khomenko, Liliia S. Paliichuk, Jose Valero, Michael Z. Zgurovsky

Анотація


In this paper we prove the existence of uniform global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of non-autonomous complex fluids.


Ключові слова


non-Newtonian fluids; parabolic equations; global attractors; infinite-dimensional dynamical systems

Повний текст:

PDF (English)

Посилання


J. M. Amigo, I. Catto, A. Gimenez, J. Valero, Attractors for a non-linear parabolic equation modelling suspension flows, Discrete Contin. Dyn. Sist., Series B, 11(2009), 205-231.

J.M. Amigo, A. Gimenez, F. Morillas, J. Valero, Attractors for a lattice dynamical system generated by non-Newtonian fluids modeling suspensions, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 20(2010), 2681-2700. DOI: 10.1142/S0218127410027295.

A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, Nauka, Moscow,

E. Cances, I. Catto, Yo. Gati, Mathematical analysis of a nonlinear parabolic equation arising in the modelling of non-Newtonian flows, SIAM J. Math. Anal., 37(2005), 60-82. DOI: 10.1137/S0036141003430044.

E. Cances, C. Le Bris, Convergence to equilibrium of a multiscale model for suspensions, Discrete Contin. Dyn. Sist., Series B, 6(2006), 449-470. DOI: 10.3934/dcdsb.2006.6.449.

V.V. Chepyzhov, M.I. Vishik, Evolution equations and their trajectory attractors, J. Math. Pures Appl., 76(1997), 913-964. DOI: 10.1016/S0021-7824(97)89978-3.

E.A. Feinberg, P.O. Kasyanov, M.Z. Zgurovsky, Uniform Fatou's lemma, J. Math. Anal. Appl., 444(2016), 550-567. DOI: 10.1016/j.jmaa.2016.06.044.

H. Gajewski, K. Groger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1975. DOI: 10.1002/mana.19750672207.

A. Gimenez, F. Morillas, J. Valero, J.M. Amig o, Stability and numerical analysis of the Hebraud-Lequeux model for suspensions, Discrete Dyn. Nat. Soc., 2011(2011), Art. ID 415921, 24 pp.

N.V. Gorban, O.V. Kapustyan, P.O. Kasyanov, Uniform trajectory attractor for non-autonomous reaction-diffusion equations with Caratheodory's nonlinearity, Nonlinear Anal., 98(2014), 13-26. DOI: 10.1016/j.na.2013.12.004.

N.V. Gorban, O.V. Kapustyan, P.O. Kasyanov, Uniform trajectory attractor for non-autonomous reaction-diffusion equations with Caratheodory's nonlinearity, Nonlinear Anal., 98(2014), 13-26. DOI: 10.1016/j.na.2013.12.004.

P. Hebraud, F. Lequeux, Mode-coupling theory for the pasty rheology of soft glassy materials, Phys. Rev. Lett., 81(1998), 2934-2937.

O.V. Kapustyan, J. Valero, P.O. Kasyanov, A. Gimenez, J.M. Amigo, Convergence of numerical approximations for a non-Newtonian model of suspensions, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 25(2015), 1540022, 24 pp.

O.V. Kapustyan, P.O. Kasyanov, J. Valero, M.Z. Zgurovsky Strong attractors for vanishing viscosity approximations of non-Newtonian suspension ows, Discrete and Continuous Dynamical Systems, 23(3) (2018), 1155-1176. DOI: 10.3934/dcdsb.2018146.

O.A. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Cambridge University Press, Cambridge, 1991.

R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1979.

R. Temam, Innite-dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988.

J. Valero, A. Gimenez, O. V. Kapustyan, P. Kasyanov, J. M. Amigo, Convergence of equilibria for numerical approximations of a suspension model, Comput. Math. Appl., 72(2016), 856-878. DOI: 10.1016/j.camwa.2016.05.034.

K. Yosida, Functional Analysis, Springer, Berlin, 1980.

M.Z. Zgurovsky, P.O. Kasyanov, J. Valero, Noncoercive evolution inclusions for Sk type operators, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 20(2010), 2823-2834. DOI: 10.1142/S0218127410027386.

M.Z. Zgurovsky, P.O. Kasyanov, O.V. Kapustyan, J. Valero, N.V. Zadoianchuk, Evolution Inclusions and variation inequalities for earth data processing III, Springer-Verlag, Berlin, 2012.

M.Z. Zgurovsky, P.O. Kasyanov, Multivalued dynamics of solutions for autonomous operator dierential equations in strongest topologies, Continuous and Distributed Systems: Theory and Applications. Solid Mechanics and Its Applications, 211(2014), 149-162.

M.Z. Zgurovsky, P.O. Kasyanov, Evolution Inclusions in Nonsmooth Systems with Applications for Earth Data Processing: Uniform Trajectory Attractors for Nonautonomous Evolution Inclusions Solutions with Pointwise Pseudomonotone Mappings, Advances in Global Optimization, Springer Proceedings in Mathematics & Statistics, 95(2015), 283-294. DOI: 10.1007/978-3-319-08377-3_28.

M.Z. Zgurovsky, P.O. Kasyanov, Uniform Trajectory Attractors for Nonautonomous Dissipative Dynamical Systems, Continuous and Distributed Systems II. Series Studies in Systems, Decision and Control, 30(2015), 221-232. DOI: 10.1007/978-3-319-19075-4_13.

M.Z. Zgurovsky, P.O. Kasyanov, Uniform Global Attractors for Nonautonomous Evolution Inclusions, Advances in Dynamical Systems and Control. Studies in Systems, Decision and Control, 69(2016). DOI: 10.1007/978-3-319-40673-2_3.

M.Z. Zgurovsky, M.O. Gluzman, N.V. Gorban, L.S. Paliichuk, O.V. Khomenko, Uniform Global Attractors for Non-Autonomous Dissipative Dynamical Systems, Discrete and Continuous Dynamical Systems, 22(5)(2017), 2053-2065. DOI: 10.3934/dcdsb.2017120.




DOI: http://dx.doi.org/10.15421/141807

Посилання

  • Поки немає зовнішніх посилань.



Індексування журналу

Журнал розміщено у наукометричних базах, репозитаріях та пошукових системах:

            


Адреса редколегії: 49050, Україна, Дніпровський національний університет імені Олеся Гончара, вул. Козакова 18, корп. 14, механіко-математичний факультет, д-р фіз.-мат. наук, проф. Когут П.І. 

email: p.kogut@i.ua

www.kdr.dp.ua

www.dnu.dp.ua


Free counters! Яндекс.Метрика

Лицензия Creative Commons
Це видання має доступ за ліцензією Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.


Open Science in Ukraine - website development