scholarly journals A PDAE formulation of parabolic problems with dynamic boundary conditions

2019 ◽  
Vol 90 ◽  
pp. 202-208 ◽  
Author(s):  
R. Altmann
Keyword(s):  
Boundary Conditions ◽  
Parabolic Problems ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals Higher-order exponential integrators for constrained semi-linear parabolic problems

2020 ◽  
Vol 2 (1) ◽  
pp. 14-20
Author(s):  
Johannes Wiedemann
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Dynamic ◽  
Order Of Convergence ◽  
Parabolic Systems ◽  
Higher Order ◽  
Parabolic Problems ◽  
Dynamic Boundary Conditions ◽  
Exponential Integrators ◽  
Dynamic Boundary

This paper provides an introduction to exponential integrators for constrained parabolic systems. In addition, building on existing results, schemes with an expected order of convergence of three and four are established and numerically tested on parabolic problems with nonlinear dynamic boundary conditions. The simulations reinforce the subjected error behaviour.

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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