Abstract
We study a mathematical model describing phase transformations in alloys with kinetics driven by mass transport and stress. To describe the dynamics, a Cahn-Hilliard system taking elastic effects into account is studied. Existence and uniqueness results for the resulting singular elliptic-parabolic system are given.
In the Cahn-Hilliard model, phase boundaries are described by a diffuse interface with small positive thickness. In the stationary case we identify the sharp interface free boundary problem that arises when the interfacial thickness tends to zero. In particular, we obtain a geometric partition problem generalizing variants of isoperimetric problems to situations where elastic interactions cannot be neglected.
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Garcke, H. (2001). Phase Boundaries in Alloys with Elastic Misfit. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8266-8_24
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DOI: https://doi.org/10.1007/978-3-0348-8266-8_24
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8266-8
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