scholarly journals A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dong Li

<p style='text-indent:20px;'>We introduce a regularization-free approach for the wellposedness of the classic Cahn-Hilliard equation with logarithmic potentials.</p>

2011 ◽  
Vol 79 (2) ◽  
pp. 561-596 ◽  
Author(s):  
Laurence Cherfils ◽  
Alain Miranville ◽  
Sergey Zelik

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Abels ◽  
Johannes Kampmann

AbstractWe rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn–Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard equation.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .


2021 ◽  
pp. 110409
Author(s):  
Gerasimos Ntoukas ◽  
Juan Manzanero ◽  
Gonzalo Rubio ◽  
Eusebio Valero ◽  
Esteban Ferrer

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