Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 89, pp. 1-17.

Title: Multi-component Allen-Cahn equation for elastically stressed solids

Authors: Thomas Blesgen (Max Planck Institute for Math., Leipzig, Germany)
         Ulrich Weikard (Univ. of Duisburg-Essen, Germany)

Abstract: 
 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.