References
- F. Bai , C.M. Elliott , A. Gardiner , A. Spence and A.M. Stuart. The viscous Cahn–Hilliard equation. I: Computations . Nonlinearity , 8 2 : 131 – 160 , 1995 . http://dx.doi.org/10.1088/0951-7715/8/2/002 .
- J. Cao , A. Chen and X. Huang . Almost periodic attractor of delayed neural networks with variable coefficients . Phys. Lett. A , 340 1–4 : 104 – 120 , 2005 . http://dx.doi.org/10.1016/j.physleta.2005.04.021 .
- R. Chill , E. Fašangová and J. Prüss . Convergence to steady states of solutions the Cahn–Hilliard and caginalp equations with dynamic boundary conditions . Math. Nachr ., 279 1314 : 1448 – 1462 , 2006 . http://dx.doi.org/10.1002/mana.200410431 .
- C.M. Elliott and A.M. Stuart Viscous Cahn–Hilliard equation. II. Analysis . J. Differential Equations , 128 2 : 387 – 414 , 1996 . http://dx.doi.org/10.1006/jdeq.1996.0101 .
- C.M. Elliott and S.M. Zheng . On the Cahn–Hilliard equation . Arch. Ration. Mech. Anal ., 96 4 : 339 – 357 , 1986 . http://dx.doi.org/10.1007/BF00251803 .
- Y. He and Y. Liu . Stability and convergence of the spectral Galerkin method for the Cahn–Hilliard equation . Numer. Methods Partial Differential Equations , 24 6 : 1485 – 1500 , 2008 . http://dx.doi.org/10.1002/num.20328 .
- B.B. King , O. Stein and M. Winkler . A fourth-order parabolic equation modeling epitaxial thin film growth . J. Math. Anal. Appl ., 286 2 : 459 – 490 , 2003 . http://dx.doi.org/10.1016/S0022-247X(03)00474-8 .
- I. Kubiaczyk and S.H. Saker . Oscillation and stability in nonlinear delay differential equations of population dynamics . Math. Comput. Modelling , 35 3–4 : 295 – 301 , 2002 . http://dx.doi.org/10.1016/S0895-7177(01)00166-2 .
- Ladyzenskaja , O. , Solonnikov , V. and Uraltseva , N. 1968 . Linear and Quasilinear Equations of Parabolic Type , Providence : American Mathematical Society .
- R. Laugesen and M. Pugh . Linear stability of steady states for thin film and Cahn–Hilliard type equations . Arch. Ration. Mech. Anal ., 154 1 : 3 – 51 , 2000 . http://dx.doi.org/10.1007/PL00004234 .
- Y. Li and J. Yin . The viscous Cahn–Hilliard equation with periodic potentials and sources . J. Fixed Point Theory Appl ., 9 1 : 63 – 84 , 2011 . http://dx.doi.org/10.1007/s11784-010-0014-z .
- Y. Li , J. Yin and C. Jin . A Cahn–Hilliard type equation with periodic gradient dependent potentials and sources . Math. Methods Appl. Sci ., 33 3 : 263 – 272 , 2010 . http://dx.doi.org/10.1002/mma.1166 .
- C. Liu A fourth order parabolic equation with nonlinear principal part . Non-linear Anal ., 68 2 : 393 – 401 , 2008 . http://dx.doi.org/10.1016/j.na.2006.11.005 .
- S. Liu , F. Wang and H. Zhao . Global existence and asymptotic of solutions of the Cahn–Hilliard equation . J. Differential Equations , 238 2 : 426 – 469 , 2007 . http://dx.doi.org/10.1016/j.jde.2007.02.014 .
- A. Miranville and A. Rougirel . Local and asymptotic analysis of the flow generated by the Cahn–Hilliard–Gurtin equations . Z. Angew. Math. Phys ., 57 2 : 244 – 268 , 2006 . http://dx.doi.org/10.1007/s00033-005-0017-6 .
- Murray , J.D. 1993 . Mathematical Biology, , second ed , Berlin : Springer-Verlag .
- B. Nicolaenko , B. Scheurer and R. Temam . Some global dynamical properties of a class of pattern formation equations . Comm. Partial Differential Equations , 14 2 : 245 – 297 , 1989 . http://dx.doi.org/10.1080/03605308908820597 .
- Novick-Cohen , A. 1988 . “ On the viscous Cahn–Hilliard equation ” . In Material Instabilities in Continuum Mechanics , 329 – 342 . New York : Oxford Univ. Press .
- C. V. Pao . Stability and attractivity of periodic solutions of parabolic systems with time delays . J. Math. Anal. Appl ., 304 2 : 423 – 450 , 2005 . http://dx.doi.org/10.1016/j.jmaa.2004.09.014 .
- P. Rybka and K. H. Hoffmann . Convergence of solutions to Cahn–Hilliard equation . Comm. Partial Differential Equations , 24 5–6 : 1055 – 1077 , 1999 . http://dx.doi.org/10.1080/03605309908821458 .
- J. Yin , Y. Li and R. Huang . The Cahn–Hilliard type equations with periodic potentials and sources . Appl. Math. Comput ., 211 1 : 211 – 221 , 2009 . http://dx.doi.org/10.1016/j.amc.2009.01.038 .
- J. Yin and Y. Wang . Asymptotic behavior of solutions for porous medium equation with periodic absorption . Int. J. Math. Math. Sci ., 26 1 : 35 – 44 , 2001 . http://dx.doi.org/10.1155/S0161171201003581 .
- L. Yin , Y. Li , R. Huang and J. Yin . Time periodic solutions for a Cahn–Hilliard type equation . Math. Comput. Modelling , 48 1 : 11 – 18 , 2008 . http://dx.doi.org/10.1016/j.mcm.2007.09.001 .