GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CAHN–HILLIARD EQUATION WITH INERTIAL TERM
Authors:
- 31 July 2012
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Mathematics
- Vol. 23 (09)
Abstract
In this paper, we investigate the Cauchy problem for Cahn–Hilliard equation with inertial term in n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, we define a solution space. Under small condition on the initial value, we prove the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces by the contraction mapping principle.Keywords
This publication has 20 references indexed in Scilit:
- GLOBAL EXISTENCE AND DECAY OF SOLUTIONS FOR A QUASI-LINEAR DISSIPATIVE PLATE EQUATIONJournal of Hyperbolic Differential Equations, 2011
- Decay property for a plate equation with memory-type dissipationKinetic and Related Models, 2011
- Global existence and asymptotic behaviorof solutions for quasi-linear dissipative plate equationDiscrete and Continuous Dynamical Systems, 2011
- A note on the optimal temporal decay estimates of solutions to the Cahn–Hilliard equationJournal of Mathematical Analysis and Applications, 2010
- Diffuse-interface model for rapid phase transformations in nonequilibrium systemsPhysical Review E, 2005
- HYPERBOLIC RELAXATION OF THE VISCOUS CAHN–HILLIARD EQUATION IN 3-DMathematical Models and Methods in Applied Sciences, 2005
- Phase-field model with relaxation of the diffusion flux in nonequilibrium solidification of a binary systemPhysics Letters A, 2001
- Stability of Cahn-Hilliard frontsCommunications on Pure and Applied Mathematics, 1999
- An L∞ bound for solutions of the Cahn-Hilliard equationArchive for Rational Mechanics and Analysis, 1995
- Free Energy of a Nonuniform System. I. Interfacial Free EnergyThe Journal of Chemical Physics, 1958