On the 3D Cahn–Hilliard equation with inertial term

Babin A., Vishik M.I.: Maximal attractors of semigroups corresponding to evolutionary differential equations. Mat. Sb., 126, 397–419 (1984)

Ball J.M.: Global attractors for damped semilinear wave equations. Partial differential equations and applications. Discrete Contin. Dyn. Syst., 10, 31–52 (2004)

Brézis H., Gallouet T.: Nonlinear Schrödinger evolution equations. Nonlinear Anal., 4, 677–681 (1980)

Cahn J.W.: On spinodal decomposition. Acta Metall., 9, 795–801 (1961)

Cahn J.W., Hilliard J.E.: Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys., 28, 258–267 (1958)

M. Conti and G. Mola, 3-D viscous Cahn–Hilliard with memory, Math. Methods Appl. Sci., (2008), doi: 10.1002/mma.1091 .

Debussche A.: A singular perturbation of the Cahn–Hilliard equation. Asymptotic Anal., 4, 161–185 (1991)

Efendiev M., Miranville A., Zelik S.: Exponential attractors for a singularly perturbed Cahn–Hilliard system. Math. Nachr., 272, 11–31 (2004)

Elliott C.M., Zheng S.: On the Cahn–Hilliard equation. Arch. Rational Mech. Anal., 96, 339–357 (1986)

P. Fabrie, C. Galusinski, A. Miranville, and A. Zelik, Uniform exponential attractors for a singularly perturbed damped wave equation, in “Partial differential equations and applications”, Discrete Contin. Dyn. Syst., 10 (2004), 211–238.

Galenko P., Jou D.: Diffuse-interface model for rapid phase transformations in nonequilibrium systems. Phys. Rev. E, 71, 046125 (2005) (13 pages)

Galenko P., Lebedev V.: Analysis of the dispersion relation in spinodal decomposition of a binary system. Philos. Mag. Lett., 87, 821–827 (2007)

Galenko P., Lebedev V.: Local nonequilibrium effect on spinodal decomposition in a binary system. Int. J. Thermodyn., 11, 21–28 (2008)

Galenko P., Lebedev V.: Nonequilibrium effects in spinodal decomposition of a binary system. Phys. Lett. A 372, 985–989 (2008)

Gatti S., Grasselli M., Miranville A., Pata V.: On the hyperbolic relaxation of the one- dimensional Cahn–Hilliard equation. J. Math. Anal. Appl. 312, 230–247 (2005)

Gatti S., Grasselli M., Miranville A., Pata V.: Hyperbolic relaxation of the viscous Cahn–Hilliard equation in 3-D. Math. Models Methods Appl. Sci. 15, 165–198 (2005)

S. Gatti, M. Grasselli, A. Miranville, and V. Pata, Memory relaxation of the one-dimensional Cahn–Hilliard equation, Dissipative phase transitions, 101–114, Ser. Adv. Math. Appl. Sci., 71, World Sci. Publ., Hackensack, NJ, 2006.

Grant C.P.: Spinodal decomposition for the Cahn–Hilliard equation. Comm. Partial Differential Equations 18, 453–490 (1993)

Grasselli M., Miranville A., Pata V., Zelik S.: Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potential. Math. Nachr. 280, 1475–1509 (2007)

Grasselli M., Schimperna G., Zelik S.: On the 2D Cahn–Hilliard equation with inertial term. Comm. Partial Differential Equation 34, 137–170 (2009)

Kania M.B.: Global attractor for the perturbed viscous Cahn–Hilliard equation. Colloq. Math. 109, 217–229 (2007)

Kenmochi N., Niezgódka M., Pawłow I.: Subdifferential operator approach to the Cahn–Hilliard equation with constraint. J. Differential Equations 117, 320–356 (1995)

Maier-Paape S., Wanner T.: Spinodal decomposition for the Cahn–Hilliard equation in higher dimensions: nonlinear dynamics. Arch. Ration. Mech. Anal. 151, 187–219 (2000)

Miranville A., Zelik S.: Robust exponential attractors for Cahn–Hilliard type equations with singular potentials. Math. Methods Appl. Sci. 27, 545–582 (2004)

Novick-Cohen A., Segel L.A.: Nonlinear aspects of the Cahn–Hilliard equation. Phys. D 10, 277–298 (1984)

Novick-Cohen A.: The Cahn–Hilliard equation: mathematical and modeling perspectives. Adv. Math. Sci. Appl. 8, 965–985 (1998)

Novick-Cohen A.: On Cahn–Hilliard type equations. Nonlinear Anal. 15, 797–814 (1990)

Nicolaenko B., Scheurer B., Temam R.: Some global dynamical properties of a class of pattern formation equations. Comm. Partial Differential Equations 14, 245–297 (1989)

Pata V., Prouse G., Vishik M.I.: Traveling waves of dissipative nonautonomous hyperbolic equations in a strip. Adv. Differential Equations 3, 249–270 (1998)

Pata V., Zelik S.: A result on the existence of global attractors for semigroups of closed operators. Commun. Pure Appl. Anal. 6, 481–486 (2007)

Rybka P., Hoffmann K.-H.: Convergence of solutions to Cahn–Hilliard equation. Comm. Partial Differential Equations 24, 1055–1077 (1999)

Segatti A.: On the hyperbolic relaxation of the Cahn–Hilliard equation in 3-D: approximation and long time behaviour. Math. Models Methods Appl. Sci. 17, 411–437 (2007)

Temam R.: “Infinite-Dimensional Dynamical Systems in Mechanics and Physics”. Springer-Verlag, New York (1997)

Vergara V.: A conserved phase field system with memory and relaxed chemical potential. J. Math. Anal. Appl. 328, 789–812 (2007)

W. von Wahl, On the Cahn–Hilliard equation u′ + Δ2 u−Δf(u) = 0, in Mathematics and mathematical engineering (Delft, 1985), Delft Progr. Rep., 10 (1985), 291–310.

Zheng S., Milani A.J.: Global attractors for singular perturbations of the Cahn–Hilliard equations. J. Differential Equations 209, 101–139 (2005)

Zheng S., Milani A.J.: Exponential attractors and inertial manifolds for singular perturbations of the Cahn–Hilliard equations. Nonlinear Anal. 57, 843–877 (2004)

Zelik S.: Asymptotic regularity of singularly perturbed damped wave equations with supercritical nonlinearities. Discrete Contin. Dyn. Syst. 11, 351–392 (2004)

Zelik S.: Global averaging and parametric resonances in damped semilinear wave equations. Proc. Roy. Soc. Edinburgh Sect. A 136, 1053–1097 (2006)