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Évolution d’une interface par capillarité et diffusion de volume. I: Existence locale en temps. (French) Zbl 0572.35051

We prove the existence locally in time for the following problem: a curve moves with velocity equal to the normal derivative of a harmonic function, whose boundary value is given by the curvature of the curve (here in the case of an initial curve graph of a smooth function).

MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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References:

[1] Baras, P.; Duchon, J.; Robert, R., Évolution d’une interface par diffusion de surface, C. R. Acad. Sc. Paris, t. 295, série I, 611-614 (1982) · Zbl 0511.35047
[2] Coudurier, L.; Eustathopoulos, N.; Gjoud, J. C.; Desre, P., Corrosion intergranulaire du cuivre par le plomb liquide sous l’effet des forces capillaires, Journal de chimie physique, t. 3, 289-294 (1977)
[3] Duchon, J.; Robert, R.; Witomski, P., Problème de Dirichlet dans l’image bilipschitzienne d’un demi-espace, Numer. Math., t. 36, 129-149 (1981) · Zbl 0462.65063
[4] Meyer, Y., Théorie du potentiel dans les domaines lipschitziens d’aprés G. C. Verchota, n° 5 (1983), Séminaire Goulaouic-Meyer-Schwartz · Zbl 0557.31004
[6] Mullins, W. W., Grain boundary grooving by volume diffusion, Transactions of the metallurgical society of AIME, t. 218, 354-361 (1960)
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