Electron. J. Diff. Eqns., Vol. 2005(2005), No. 89, pp. 1-17.

Multi-component Allen-Cahn equation for elastically stressed solids

Thomas Blesgen, Ulrich Weikard

The vector-valued Allen-Cahn equations are combined with elasticity where a linear stress-strain relationship is assumed. A short physical derivation of the generalised model is given and global existence and uniqueness of the solution are shown under suitable growth conditions on the nonlinearity.

Submitted November 18, 2004. Published August 15, 2005.
Math Subject Classifications: 35K15, 74B10, 74N20.
Key Words: Linear elasticity; modeling and simulation of multiscale problems.

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Thomas Blesgen
Max Planck Institute for Mathematics in the Sciences
Inselstrasse 22-26, 04103 Leipzig, Germany
email: blesgen@mis.mpg.de
Ulrich Weikard
Faculty of Mathematics, University of Duisburg-Essen
Lotharstrasse 65, 47048 Duisburg, Germany
email: wkd@math.uni-duisburg.de

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