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Volume 14, Issue 2
An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy

C. Kahle

Int. J. Numer. Anal. Mod., 14 (2017), pp. 243-254.

Published online: 2016-05

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  • Abstract

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.

  • Keywords

Cahn-Hilliard, Moreau-Yosida relaxation, phase field equations, uniform bounds.

  • AMS Subject Headings

35Q35, 35B45, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-14-243, author = {}, title = {An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {14}, number = {2}, pages = {243--254}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/419.html} }
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 -

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.

C. Kahle. (2019). An $L^∞$ Bound for the Cahn-Hilliard Equation with Relaxed Non-Smooth Free Energy. International Journal of Numerical Analysis and Modeling. 14 (2). 243-254. doi:
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