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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
Wuhan University
Latest Article
Global Existence and Lp Decay Esti-mate of Solutions for Viscous Cahn-Hilliard Equation with Inertial Term
XU Hongmei, SHI Yu
College of Science, Hohai University, Nanjing 211100, Jiangsu, China
In this paper, Cauchy problem of viscous Cahn-Hil-liard equation with inertial term in multi-space dimension is considered. Based on the detailed analysis of Green function, using fixed point theorem, we get the global in-time existence of classical solution. Furthermore, we get Lp decay rate of the solution.
Key words:Cahn-Hilliard equation with inertial term; global existence of classical solution; decay estimate; fixed point theorem
CLC number:O 175.28
[1]	Caffarelli L A, Muler N E. An  -bound for solutions of the Cahn-Hilliard equation [J]. Arch Ration Mech Anal, 1995, 133(2): 129-144.
[2]	Efendiev M, Miranville A, Zelik S. Exponential attractors for a singularly perturbed Cahn-Hilliard system [J]. Math Nachr, 2004, 272(1): 11-31.
[3]	Elhott C M, Zheng S. On the Cahn-Hilliard equation [J]. Arch Ration Mech Anal, 1986, 96(4): 339-357.
[4]	Novick-Cohen A. The Cahn-Hilliard equation mathematical and modeling perspectives [J]. Adv Math Sci Appl, 1998, 8: 965-985.
[5]	Novick-Cohen A. On Cahn-Hilliard type equations [J]. Non-linear Anal, 1990, 15(9): 797-814.
[6]	Galenko P. Phase-field model with relaxation of the diffusion flux in nonequilibrium solidification of a binary system [J]. Phys Lett A, 2001, 287(3-4): 190-197.
[7]	Galenko P, Jou D. Diffuse-interface model for rapid phase transformations in nonequilibrium systems [J]. Phys Rev E, 2005, 71(4): 046125.
[8]	Galenko P, Lebedev V. Analysis of the dispersion relation in spinodal decomposition of a binary system [J]. Philos Mag Lett, 2007, 87(11): 821-827.
[9]	Galenko P, Lebedev V. Local nonequilibrium effect on spi-nodal decomposition in a binary system [J]. Int J Thermodyn, 2008, 11(1): 21-28.
[10]	Grasselli M, Schimperna G, Segatti A, et al. On the 3D Cahn-Hilliard equation with inertial term [J]. J Evol Equ, 2009, 9(2): 371-404.
[11]	Grasselli M G, Zelik S. On the 2D Cahn-Hilliard equation with inertial term [J]. Commun Partial Diff Eqns, 2009, 34(2): 137-170.
[12]	Wang W K, Wu Z G. Optimal decay rate of solutions for Cahn-Hilliard equation with inertial term in multi-dimensions [J]. J Math Anal Appl, 2012, 387(1): 349-358.
[13]	Deng S J, Wang W K, Zhao H L. Existence theory and   estimates for the solution of nonlinear viscous wave equation [J]. Nonlinear Anulysis-real world Applications, 2010, 11(5): 4404-4414.
[14]	Li T T, Chen Y M. The Nonlinear Evolution Euqation [M]. Beijing: Scientific Press, 1989 (Ch).
[15]	Wang W K, Wang W J. The pointwise estimates of solutions for semilinear dissipative wave equation in multi-dimension [J]. Jourral of Nathervatical Analysis and Applications, 2010, 366(1): 226-241.
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