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Path-following the equilibria of the Cahn–Hilliard equation on the square

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Computing and Visualization in Science

Abstract.

We numerically calculate the equilibria of the Cahn-Hilliard equation on the unit square by a path-following algorithm. The solutions we find form two-dimensional manifolds in a three-dimensional parameter space. From these data bifurcation diagrams for selected values of the mean mass are calculated and plotted against the energy of our problem.

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Authors and Affiliations

  1. Institut für Mathematik, RWTH Aachen, Templergraben 55, 52062 Aachen, Germany (http://www.instmath.rwth-aachen.de/˜maier), , , , , , DE

    Stanislaus Maier-Paape

  2. Institut für Mathematik, Universität Augsburg, Universitätsstrasse 14, D-86135 Augsburg, Germany, , , , , , DE

    Ulrich Miller

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  1. Stanislaus Maier-Paape
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  2. Ulrich Miller
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Received: 10 September 2000 / Accepted: 1 February 2001

Communicated by G. Wittum

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Maier-Paape, S., Miller, U. Path-following the equilibria of the Cahn–Hilliard equation on the square. Comput Visual Sci 5, 115–138 (2002). https://doi.org/10.1007/s00791-002-0095-3

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  • DOI: https://doi.org/10.1007/s00791-002-0095-3

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