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Volumn 2, Issue 4, 2000, Pages 361-379

On convergence of solutions of the crystalline Stefan problem with Gibbs-Thomson law and kinetic undercooling

Author keywords

Crystalline anisotropy; Free boundary; Gibbs Thomson law; Stefan problem

Indexed keywords


EID: 0009762070     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/25     Document Type: Article
Times cited : (5)

References (17)
  • 1
    • 0001861231 scopus 로고    scopus 로고
    • Mathematical existence of crystal growth with Gibbs-Thomson curvature effects
    • ALMGREN, F. & WANG, L. Mathematical existence of crystal growth with Gibbs-Thomson curvature effects. J. Geom. Anal. 10, (2000) 1-100.
    • (2000) J. Geom. Anal , vol.10 , pp. 1-100
    • Almgren, F.1    Wang, L.2
  • 2
    • 84906890283 scopus 로고
    • Growth of faceted needle crystals: Theory
    • BEN AMAR, & POMEAU, Y. Growth of faceted needle crystals: theory. Europhys. Lett. 6, (1988) 609-614.
    • (1988) Europhys. Lett , vol.6 , pp. 609-614
    • Amar, B.1    Pomeau, Y.2
  • 3
    • 84971505912 scopus 로고    scopus 로고
    • Facet-breaking for three-dimensional crystals evolving by mean curvature
    • BELLETTINI, G., NOVAGA, M., & PAOLINI, M. Facet-breaking for three-dimensional crystals evolving by mean curvature. Interfaces and Free Boundaries 1, (1999) 39-56.
    • (1999) Interfaces and Free Boundaries , vol.1 , pp. 39-56
    • Bellettini, G.1    Novaga, M.2    Paolini, M.3
  • 4
    • 0001304426 scopus 로고
    • Local existence and uniqueness of solutions to the Stefan problem with surface tension and kinetic undercooling
    • CHEN, X. & REITICH, F. Local existence and uniqueness of solutions to the Stefan problem with surface tension and kinetic undercooling. J. Math. Anal. Appl. 164, (1992) 350-362.
    • (1992) J. Math. Anal. Appl , vol.164 , pp. 350-362
    • Chen, X.1    Reitich, F.2
  • 5
    • 0009423784 scopus 로고    scopus 로고
    • A subdiffential interpretation of crystalline motion under nonuniform driving force
    • CHEN, W. & HU, S. eds, Southwest Missouri State University, Springfield, MO
    • GIGA, M.-H. & GIGA, Y. A subdiffential interpretation of crystalline motion under nonuniform driving force. In: CHEN, W. & HU, S. (eds), Proc. International Conference on Dynamical Systems and Differential Equations, vol. I. pp. 276-287. Southwest Missouri State University, Springfield, MO (1998).
    • (1998) Proc. International Conference on Dynamical Systems and Differential Equations , vol.1 , pp. 276-287
    • Giga, M.-H.1    Giga, Y.2
  • 7
    • 0029170803 scopus 로고
    • Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces
    • GURTIN, M. & MATIAS, J. Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces. Quart. Appl. Math. 53, (1995) 761-782.
    • (1995) Quart. Appl. Math , vol.53 , pp. 761-782
    • Gurtin, M.1    Matias, J.2
  • 8
    • 0003460899 scopus 로고
    • Lecture Notes in Mathematics, 840. Springer, Berlin, Russian translation: Mir, Moscow
    • HENRY, D. Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, 840. Springer, Berlin (1981) (Russian translation: Mir, Moscow 1985).
    • (1981) Geometric Theory of Semilinear Parabolic Equations
    • Henry, D.1
  • 9
    • 23244465575 scopus 로고
    • Surface tension as a motivation for sintering
    • KINGSTON, W. E. ed, McGraw-Hill, New York
    • HERRING, C. Surface tension as a motivation for sintering. In: KINGSTON, W. E. (ed), The Physics of Powder Metallurgy. McGraw-Hill, New York (1958).
    • (1958) The Physics of Powder Metallurgy
    • Herring, C.1
  • 10
    • 84971922508 scopus 로고
    • Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature
    • LUCKHAUS, S. Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature. Euro. J. Appl. Math. 1, (1990) 101-111.
    • (1990) Euro. J. Appl. Math , vol.1 , pp. 101-111
    • Luckhaus, S.1
  • 11
    • 0001427453 scopus 로고
    • The Gibbs-Thomson correction and condition for the existence of classical solution of the modified Stefan problem
    • RADKEVICH, E. V. The Gibbs-Thomson correction and condition for the existence of classical solution of the modified Stefan problem. Soviet Math. Dokl. 43, (1991) 274-278.
    • (1991) Soviet Math. Dokl , vol.43 , pp. 274-278
    • Radkevich, E.V.1
  • 12
    • 0009762227 scopus 로고
    • A quasi-steady approximation to an integro-differential model of interface motion
    • RYBKA, P. A quasi-steady approximation to an integro-differential model of interface motion. Appl. Anal. 56, (1995) 19-34.
    • (1995) Appl. Anal , vol.56 , pp. 19-34
    • Rybka, P.1
  • 13
    • 0031077374 scopus 로고    scopus 로고
    • A crystalline motion: Uniqueness and geometric properties
    • RYBKA, P. A crystalline motion: uniqueness and geometric properties. SIAM J. Appl. Math. 57, (1997) 53-72.
    • (1997) SIAM J. Appl. Math , vol.57 , pp. 53-72
    • Rybka, P.1
  • 14
    • 0000962869 scopus 로고    scopus 로고
    • Crystalline version of the Stefan problem with Gibbs-Thomson law and kinetic undercooling
    • RYBKA, P. Crystalline version of the Stefan problem with Gibbs-Thomson law and kinetic undercooling. Adv. Differential Equations 3, (1998) 687-713.
    • (1998) Adv. Differential Equations , vol.3 , pp. 687-713
    • Rybka, P.1
  • 15
    • 0033243610 scopus 로고    scopus 로고
    • The crystalline version of the modified Stefan problem in the plane and its properties
    • electronic
    • RYBKA, P. The crystalline version of the modified Stefan problem in the plane and its properties. SIAM J. Math. Anal. 30, (1999) 756-786. (electronic).
    • (1999) SIAM J. Math. Anal , vol.30 , pp. 756-786
    • Rybka, P.1
  • 16
    • 34249757566 scopus 로고
    • Convergence of the phase-field equations to the Mullins-Sekerka problem with kinetic undercooling
    • SONER, H. M. Convergence of the phase-field equations to the Mullins-Sekerka problem with kinetic undercooling. Arch. Ration. Mech. Anal. 131, (1995) 134-197.
    • (1995) Arch. Ration. Mech. Anal , vol.131 , pp. 134-197
    • Soner, H.M.1
  • 17
    • 0001664793 scopus 로고
    • Motion of curves by crystalline curvature, including triple junctions and boundary points
    • TAYLOR, J. E. Motion of curves by crystalline curvature, including triple junctions and boundary points. Proc. Symp. Pure Math. 54, (1993) 417-438.
    • (1993) Proc. Symp. Pure Math , vol.54 , pp. 417-438
    • Taylor, J.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.