Abstract
The use of parabolic double obstacles problems for approximating curvature dependent phase boundary motion is reviewed. It is shown that such problems arise naturally in multi-component diffusion with capillarity. Formal matched asymptotic expansions are employed to show that phase field models with order parameter solving an obstacle problem approximate curvature dependent phase boundary motion. Numerical simulations of surfaces evolving according to their mean curvature are presented.
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Blowey, J.F., Elliott, C.M. (1993). Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems. In: Ni, WM., Peletier, L.A., Vazquez, J.L. (eds) Degenerate Diffusions. The IMA Volumes in Mathematics and its Applications, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0885-3_2
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DOI: https://doi.org/10.1007/978-1-4612-0885-3_2
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