Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

H. Mete Soner

doi:10.1007/BF00386194

Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

H. Mete Soner

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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.

Original language	English (US)
Pages (from-to)	139-197
Number of pages	59
Journal	Archive for Rational Mechanics and Analysis
Volume	131
Issue number	2
DOIs	https://doi.org/10.1007/BF00386194
State	Published - Jun 1 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/BF00386194

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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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N2 - 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.

AB - 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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Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

Abstract

All Science Journal Classification (ASJC) codes

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