Geodesic
Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
Applications of Mathematics, Tome 60 (2015) no. 1, pp. 51-90.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We show existence of solutions to two types of generalized anisotropic Cahn-Hilliard problems: In the first case, we assume the mobility to be dependent on the concentration and its gradient, where the system is supplied with dynamic boundary conditions. In the second case, we deal with classical no-flux boundary conditions where the mobility depends on concentration $u$, gradient of concentration $\nabla u$ and the chemical potential $\Delta u-s'(u)$. The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.
DOI : 10.1007/s10492-015-0085-7
Classification : 35D30, 35K57, 47J35, 80A22
Keywords: Cahn-Hilliard; anisotropic behavior; gradient flow; curve of maximal slope; entropy 
@article{10_1007_s10492_015_0085_7,
     author = {Heida, Martin},
     title = {Existence of solutions for two types of generalized versions of the {Cahn-Hilliard} equation},
     journal = {Applications of Mathematics},
     pages = {51--90},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {2015},
     doi = {10.1007/s10492-015-0085-7},
     mrnumber = {3299873},
     zbl = {06391462},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0085-7/}
}
TY  - JOUR
AU  - Heida, Martin
TI  - Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
JO  - Applications of Mathematics
PY  - 2015
SP  - 51
EP  - 90
VL  - 60
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0085-7/
DO  - 10.1007/s10492-015-0085-7
LA  - en
ID  - 10_1007_s10492_015_0085_7
ER  - 
%0 Journal Article
%A Heida, Martin
%T Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
%J Applications of Mathematics
%D 2015
%P 51-90
%V 60
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0085-7/
%R 10.1007/s10492-015-0085-7
%G en
%F 10_1007_s10492_015_0085_7
Heida, Martin. Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation. Applications of Mathematics, Tome 60 (2015) no. 1, pp. 51-90. doi : 10.1007/s10492-015-0085-7. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0085-7/

Cité par Sources :