An asymptotic solution was constructed for a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and it was shown that when a regularity parameter tended to zero, this solution converged to the solution for a sharp-interface model which described the phase interface in an elastically deformable solid moving by interface diffusion. Therefore, the coupled system could be used as a diffusive interface model. Unlike diffusive interface models based upon the Cahn–Hilliard equation, the interface diffusion was driven solely by the bulk energy. Hence the Laplacian of the curvature was not part of the driving force. Also, no re-scaling of the parabolic equation was necessary. Since the asymptotic solution did not solve the system exactly, the proof was considered to be formal.

Interface Motion by Interface Diffusion Driven by Bulk Energy: Justification of a Diffusive Interface Model. H.D.Alber, P.Zhu: Continuum Mechanics and Thermodynamics, 2011, 23[2], 139-76