scholarly journals On the accurate long-time solution of the wave equation in exterior domains: asymptotic expansions and corrected boundary conditions

1994 ◽  
Vol 63 (208) ◽  
pp. 507 ◽  
Author(s):  
Thomas Hagstrom ◽  
S. I. Hariharan ◽  
R. C. MacCamy
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Asymptotic Expansions ◽  
Exterior Domains ◽  
Time Solution ◽  
Long Time

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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