Global existence and $L_p$ decay estimate of solution for Cahn-Hilliard equation with inertial term

2021 ◽  
pp. 1-15
Author(s):  
Hongmei Xu ◽  
Qi Li
Keyword(s):  
Global Existence ◽  
Decay Estimate ◽  
Inertial Term ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CAHN–HILLIARD EQUATION WITH INERTIAL TERM

2012 ◽  
Vol 23 (09) ◽  
pp. 1250087 ◽  
Author(s):  
YIN-XIA WANG ◽  
ZHIQIANG WEI
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Dimensional Space ◽  
Solution Space ◽  
Contraction Mapping Principle ◽  
Asymptotic Behavior Of Solutions ◽  
Inertial Term ◽  
Hilliard Equation ◽  
The Cauchy Problem ◽  
Cahn Hilliard Equation

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.

scholarly journals On the 3D Cahn–Hilliard equation with inertial term

2009 ◽  
Vol 9 (2) ◽  
pp. 371-404 ◽  
Author(s):  
Maurizio Grasselli ◽  
Giulio Schimperna ◽  
Antonio Segatti ◽  
Sergey Zelik
Keyword(s):  
Inertial Term ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals Pointwise Estimates of Solutions for the Viscous Cahn-Hilliard Equation with Inertial Term

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Nianying Li ◽  
Li Yin ◽  
Honglian You
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Pointwise Estimates ◽  
Inertial Term ◽  
Estimates Of Solutions ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

In this paper, we study the pointwise estimates of solutions to the viscous Cahn-Hilliard equation with the inertial term in multidimensions. We use Green’s function method. Our approach is based on a detailed analysis on the Green’s function of the linear system. And we get the solution’s Lp convergence rate.

scholarly journals Cahn–Hilliard equations incorporating elasticity: analysis and comparison to experiments

2013 ◽  
Vol 371 (2005) ◽  
pp. 20120342 ◽  
Author(s):  
Thomas Blesgen ◽  
Isaac Vikram Chenchiah
Keyword(s):  
Energy Density ◽  
Global Existence ◽  
Three Dimensions ◽  
Elasticity Analysis ◽  
Micro Structure ◽  
Existence Of Weak Solutions ◽  
Hilliard Equation ◽  
Elastic Energy Density ◽  
Theoretical Predictions ◽  
Cahn Hilliard Equation

We consider a generalization of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasi-convex, incorporates micro-structure formation on smaller length scales. We explore the global existence of weak solutions in two and three dimensions. We compare theoretical predictions with experimental observations of coarsening in superalloys.

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