On the unique solvability of a nonlocal phase separation problem for multicomponent systems

Jens A. Griepentrog. "On the unique solvability of a nonlocal phase separation problem for multicomponent systems." Banach Center Publications 66.1 (2004): 153-164. <http://eudml.org/doc/281681>.

@article{JensA2004,
abstract = {A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential differences. Applying fixed-point arguments and comparison principles we prove the existence of variational solutions in standard Hilbert spaces for evolution systems. Moreover, using some regularity theory for parabolic boundary value problems in Hölder spaces we get the unique solvability of our problem. We conclude our considerations with the presentation of simulation results for a ternary system.},
author = {Jens A. Griepentrog},
journal = {Banach Center Publications},
keywords = {nonlocal phase separation models; Cahn-Hilliard equation; initial boundary value problems; nonlinear evolution equations; regularity theory},
language = {eng},
number = {1},
pages = {153-164},
title = {On the unique solvability of a nonlocal phase separation problem for multicomponent systems},
url = {http://eudml.org/doc/281681},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Jens A. Griepentrog
TI - On the unique solvability of a nonlocal phase separation problem for multicomponent systems
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 153
EP - 164
AB - A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential differences. Applying fixed-point arguments and comparison principles we prove the existence of variational solutions in standard Hilbert spaces for evolution systems. Moreover, using some regularity theory for parabolic boundary value problems in Hölder spaces we get the unique solvability of our problem. We conclude our considerations with the presentation of simulation results for a ternary system.
LA - eng
KW - nonlocal phase separation models; Cahn-Hilliard equation; initial boundary value problems; nonlinear evolution equations; regularity theory
UR - http://eudml.org/doc/281681
ER -