scholarly journals Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions

2006 ◽  
Vol 185 (4) ◽  
pp. 627-648 ◽  
Author(s):  
Jan Prüss ◽  
Reinhard Racke ◽  
Songmu Zheng
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Maximal Regularity ◽  
Asymptotic Behavior Of Solutions ◽  
Dynamic Boundary Conditions ◽  
Hilliard Equation ◽  
Dynamic Boundary ◽  
Cahn Hilliard Equation

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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