TY - JOUR
T1 - An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 243
EP - 254
PY - 2016
DA - 2016/05
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/419.html
KW - Cahn-Hilliard, Moreau-Yosida relaxation, phase field equations, uniform bounds.
AB - <p style="text-align: justify;">Phase field models are widely used to describe multiphase systems. Here a smooth
indicator function, called phase field, is used to describe the spatial distribution of the phases
under investigation. Material properties like density or viscosity are introduced as given functions
of the phase field. These parameters typically have physical bounds to fulfil, e.g. positivity of the
density. To guarantee these properties, uniform bounds on the phase field are of interest. In this
work we derive a uniform bound on the solution of the Cahn-Hilliard system, where we use the
double-obstacle free energy, that is relaxed by Moreau-Yosida relaxation.</p>