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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
A sharp interface model for the propagation of martensitic phase boundaries
Patrick W. Dondl and Kaushik BhattacharyaAbstract
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.
- Received:
- 26.11.08
- Published:
- 05.12.08
- MSC Codes:
- 35A15, 49Q20
- PACS:
- 81.30.Kf
- Keywords:
- calculus of variations, Martensitic Phase Boundaries, Free Boundary Evolution