scholarly journals Time-periodic solution for a fourth-order parabolic equation describing crystal surface growth

2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Bo Liu ◽  
Ning Duan
Keyword(s):  
Periodic Solution ◽  
Parabolic Equation ◽  
Fourth Order ◽  
Crystal Surface ◽  
Surface Growth ◽  
Order Parabolic Equation ◽  
Fourth Order Parabolic Equation ◽  
Time Periodic ◽  
Time Periodic Solution

scholarly journals Global dynamics of a fourth-order parabolic equation describing crystal surface growth

2019 ◽  
Vol 24 (2) ◽  
pp. 159-175 ◽  
Author(s):  
Ning Duan ◽  
Xianyun Xu
Keyword(s):  
Parabolic Equation ◽  
Global Attractor ◽  
Fourth Order ◽  
Crystal Surface ◽  
Surface Growth ◽  
Global Dynamics ◽  
Initial Value ◽  
Order Parabolic Equation ◽  
Fourth Order Parabolic Equation

In this paper, we study the global dynamics for the solution semiflow of a fourth-order parabolic equation describing crystal surface growth. We show that the equation has a global attractor in H4per(Ω) when the initial value belongs to H1per(Ω).

On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Ning Duan ◽  
Xiaopeng Zhao ◽  
Xiufang Zhao
Keyword(s):  
Thin Film ◽  
Parabolic Equation ◽  
Fourth Order ◽  
Film Growth ◽  
Thin Film Growth ◽  
Equation Modeling ◽  
Epitaxial Thin Film ◽  
Epitaxial Thin Film Growth ◽  
Order Parabolic Equation ◽  
Fourth Order Parabolic Equation

AbstractIn this paper, we study the existence and uniqueness of global weak solution, the regularity of the solutions and the existence of global attractor for a fourth order parabolic equation modeling epitaxial thin film growth with Neumann boundary conditions in two space dimensions.

A coupling method based on new MFE and FE for fourth-order parabolic equation

2013 ◽  
Vol 43 (1-2) ◽  
pp. 249-269 ◽  
Author(s):  
Yang Liu ◽  
Zhichao Fang ◽  
Hong Li ◽  
Siriguleng He ◽  
Wei Gao
Keyword(s):  
Parabolic Equation ◽  
Fourth Order ◽  
Coupling Method ◽  
Order Parabolic Equation ◽  
Fourth Order Parabolic Equation
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