Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation

Martin Heida

Applications of Mathematics (2015)

  • Volume: 60, Issue: 1, page 51-90
  • ISSN: 0862-7940

Abstract

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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 ∇ u and the chemical potential Δ u - s ' ( u ) . The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.

How to cite

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Heida, Martin. "Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation." Applications of Mathematics 60.1 (2015): 51-90. <http://eudml.org/doc/262195>.

@article{Heida2015,
abstract = {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 $\Delta u-s^\{\prime \}(u)$. The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.},
author = {Heida, Martin},
journal = {Applications of Mathematics},
keywords = {Cahn-Hilliard; anisotropic behavior; gradient flow; curve of maximal slope; entropy; Cahn-Hilliard equation; anisotropic behavior; gradient flow; curve of maximal slope; entropy},
language = {eng},
number = {1},
pages = {51-90},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation},
url = {http://eudml.org/doc/262195},
volume = {60},
year = {2015},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 51
EP - 90
AB - 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 $\Delta u-s^{\prime }(u)$. The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures.
LA - eng
KW - Cahn-Hilliard; anisotropic behavior; gradient flow; curve of maximal slope; entropy; Cahn-Hilliard equation; anisotropic behavior; gradient flow; curve of maximal slope; entropy
UR - http://eudml.org/doc/262195
ER -

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