Abstract
I prove that the solutions of the phase-field equations, on a subsequence, converge to a weak solution of the Mullins-Sekerka problem with kinetic undercooling. The method is based on energy estimates, a monotonicity formula, and the equipartition of the energy at each time. I also show that for almost all t, the limiting interface is (d − 1)-rectifiable with a square-integrable mean-curvature vector.
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Dedicated to Mort Gurtin on the occasion of his sixtieth birthday
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Soner, H.M. Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling. Arch. Rational Mech. Anal. 131, 139–197 (1995). https://doi.org/10.1007/BF00386194
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DOI: https://doi.org/10.1007/BF00386194