Multi-component Allen-Cahn equation for elastically stressed solids
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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.
CitationBlesgen, T., & Weikard, U. (2005). Multi-component Allen-Cahn equation for elastically stressed solids. Electronic Journal of Differential Equations, 2005(89), pp. 1-17.
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