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Volumn 56, Issue 1, 2003, Pages 139-161

The Stefan problem with nonlinear kinetic undercooling

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; INITIAL VALUE PROBLEMS; ONE DIMENSIONAL; OXIDATION; REACTION KINETICS; SILICON; TWO DIMENSIONAL;

EID: 0037293195     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/56.1.139     Document Type: Article
Times cited : (19)

References (42)
  • 1
    • 0034250733 scopus 로고    scopus 로고
    • Asymptotic results for the Stefan problem with kinetic undercooling
    • J. D. Evans and J. R. King, Asymptotic results for the Stefan problem with kinetic undercooling, Q. Jl Mech. Appl. Math. 53 (2000) 449-473.
    • (2000) Q. Jl Mech. Appl. Math. , vol.53 , pp. 449-473
    • Evans, J.D.1    King, J.R.2
  • 2
    • 0001678143 scopus 로고
    • Kinetics of crystal growth from silicate melts: Anorthite and diopside
    • R. J. Kirkpatrick, G. R. Robinson and J. F. Hays, Kinetics of crystal growth from silicate melts: Anorthite and diopside, J. Geophys. Res. 81 (1976) 5715-5720.
    • (1976) J. Geophys. Res. , vol.81 , pp. 5715-5720
    • Kirkpatrick, R.J.1    Robinson, G.R.2    Hays, J.F.3
  • 3
    • 0028156047 scopus 로고
    • The transient-behaviour of alloys solidified from below prior to the formation of chimneys
    • M. G. Worster and R. C. Kerr, The transient-behaviour of alloys solidified from below prior to the formation of chimneys, J. Fluid Mech. 269 (1994) 23-44.
    • (1994) J. Fluid Mech. , vol.269 , pp. 23-44
    • Worster, M.G.1    Kerr, R.C.2
  • 4
    • 0012251009 scopus 로고
    • Some remarks on non-equilibrium solidification problems
    • (ed. K. H. Hoffman and J. Sprekels; Pitman, London)
    • A. B. Crowley, Some remarks on non-equilibrium solidification problems, Free and Moving Boundary Problems (ed. K. H. Hoffman and J. Sprekels; Pitman, London 1989).
    • (1989) Free and Moving Boundary Problems
    • Crowley, A.B.1
  • 5
    • 0018231011 scopus 로고
    • Sample-dimension effects in the sorption of solvents in polymers - A mathematical model
    • G. Astarita and S. Joshi, Sample-dimension effects in the sorption of solvents in polymers - A mathematical model, J. Membrane Sci. 4 (1978) 165-182.
    • (1978) J. Membrane Sci. , vol.4 , pp. 165-182
    • Astarita, G.1    Joshi, S.2
  • 6
    • 0017957201 scopus 로고
    • A class of mathematical models for sorption of swelling solvents in glassy polymers
    • ____ and G. C. Sarti, A class of mathematical models for sorption of swelling solvents in glassy polymers, Polymer Eng. Sci. 18 (1978) 388-395.
    • (1978) Polymer Eng. Sci. , vol.18 , pp. 388-395
    • Astarita, G.1    Joshi, S.2    Sarti, G.C.3
  • 7
    • 0012248476 scopus 로고
    • A class of free boundary problems arising in the analysis of transport phenomena in polymers
    • (ed. A. Fasano and M. Primicerio; Pitman, London)
    • ____, A class of free boundary problems arising in the analysis of transport phenomena in polymers, Free Boundary Problems: Theory and Applications, II (ed. A. Fasano and M. Primicerio; Pitman, London 1983) 602-612.
    • (1983) Free Boundary Problems: Theory and Applications, II , pp. 602-612
    • Astarita, G.1    Joshi, S.2    Sarti, G.C.3
  • 9
    • 0024139247 scopus 로고
    • Free boundary problems in controlled release pharmaceuticals. I: Diffusion in glassy polymers
    • D. S. Cohen and T. Erneux, Free boundary problems in controlled release pharmaceuticals. I: Diffusion in glassy polymers, SIAM J. Appl. Math. 48 (1988) 1451-1465.
    • (1988) SIAM J. Appl. Math. , vol.48 , pp. 1451-1465
    • Cohen, D.S.1    Erneux, T.2
  • 10
    • 0000233647 scopus 로고
    • The isolation oxidation of silicon
    • J. R. King, The isolation oxidation of silicon, ibid. 49 (1989) 264-280.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 264-280
    • King, J.R.1
  • 12
    • 0000877960 scopus 로고
    • A revised model for the oxidation of silicon by oxygen
    • J. Blanc, A revised model for the oxidation of silicon by oxygen, Appl. Phys. Lett. 33 (1978) 424-426.
    • (1978) Appl. Phys. Lett. , vol.33 , pp. 424-426
    • Blanc, J.1
  • 13
    • 0000741037 scopus 로고
    • New oxide growth law and the thermal oxidation of silicon
    • S. M. Hu, New oxide growth law and the thermal oxidation of silicon, ibid. 42 (1983) 872-874.
    • (1983) Appl. Phys. Lett. , vol.42 , pp. 872-874
    • Hu, S.M.1
  • 14
    • 0034481839 scopus 로고    scopus 로고
    • On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model
    • J. D. Evans and J. R. King, On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model, SIAM J. Appl. Math. 60 (2000) 1977-1996.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1977-1996
    • Evans, J.D.1    King, J.R.2
  • 15
    • 0012340839 scopus 로고
    • Thermal oxidation of silicon: Chemisorption and linear rate constant
    • S. M. Hu, Thermal oxidation of silicon: chemisorption and linear rate constant, J. Appl. Phys. 54 (1984) 1069-1075.
    • (1984) J. Appl. Phys. , vol.54 , pp. 1069-1075
    • Hu, S.M.1
  • 16
    • 0003102077 scopus 로고
    • Fully time-dependent theory for the growth of spherical crystal nuclei
    • R. J. Schaefer and M. E. Glicksman, Fully time-dependent theory for the growth of spherical crystal nuclei, J. Crystal Growth 5 (1969) 44-58.
    • (1969) J. Crystal Growth , vol.5 , pp. 44-58
    • Schaefer, R.J.1    Glicksman, M.E.2
  • 17
    • 0000808009 scopus 로고
    • Growth from a hypercooled melt near absolute stability
    • A. Umantsev and S. H. Davis, Growth from a hypercooled melt near absolute stability, Physical Rev. A. 45 (1992) 7195-7201.
    • (1992) Physical Rev. A. , vol.45 , pp. 7195-7201
    • Umantsev, A.1    Davis, S.H.2
  • 18
    • 36849117884 scopus 로고
    • Morphological stability of a particle growing by diffusion or heat flow
    • W. W. Mullins and R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34 (1963) 323-329.
    • (1963) J. Appl. Phys. , vol.34 , pp. 323-329
    • Mullins, W.W.1    Sekerla, R.F.2
  • 19
    • 0342583796 scopus 로고
    • Instabilities and pattern formation in crystal growth
    • J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52 (1980) 1-28.
    • (1980) Rev. Mod. Phys. , vol.52 , pp. 1-28
    • Langer, J.S.1
  • 20
    • 0002647116 scopus 로고
    • The stabilizing effect of surface tension on the development of the free boundary in a planar, one-dimensional, Cauchy-Stefan problem
    • J. Chadam and P. Ortoleva, The stabilizing effect of surface tension on the development of the free boundary in a planar, one-dimensional, Cauchy-Stefan problem, IMA J. Appl. Math. 30 (1983) 57-66.
    • (1983) IMA J. Appl. Math. , vol.30 , pp. 57-66
    • Chadam, J.1    Ortoleva, P.2
  • 21
    • 0002041075 scopus 로고
    • Existence and stability for spherical crystals growing in a supersaturated solution
    • ____, S. D. Howison and P. Ortoleva, Existence and stability for spherical crystals growing in a supersaturated solution, ibid. 39 (1987) 1-15.
    • (1987) IMA J. Appl. Math. , vol.39 , pp. 1-15
    • Chadam, J.1    Howison, S.D.2    Ortoleva, P.3
  • 22
    • 84971922508 scopus 로고
    • Solutions for the two-phase Stefan problem with the Gibbs-Thomson law for the melting temperature
    • S. Luckhaus, 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
  • 23
    • 0012302002 scopus 로고
    • Initiation of shape instabilities of free boundaries in planar Cauchy-Stefan problems
    • Q. Zhu, A. Peirce and J. Chadam, Initiation of shape instabilities of free boundaries in planar Cauchy-Stefan problems, ibid. 4 (1993) 419-436.
    • (1993) Euro. J. Appl. Math. , vol.4 , pp. 419-436
    • Zhu, Q.1    Peirce, A.2    Chadam, J.3
  • 24
    • 0002114547 scopus 로고    scopus 로고
    • A Stefan-like problem with a kinetic condition and surface tension effects
    • S. H. Doole, A Stefan-like problem with a kinetic condition and surface tension effects, Math. Comput. Modelling 23 (1996) 55-67.
    • (1996) Math. Comput. Modelling , vol.23 , pp. 55-67
    • Doole, S.H.1
  • 25
    • 0031172964 scopus 로고    scopus 로고
    • Global existence and asymptotic behavior for the radially symmetric case of a two-phase Stefan problem with interfacial energy
    • G. Scianna, Global existence and asymptotic behavior for the radially symmetric case of a two-phase Stefan problem with interfacial energy, J. Math. Anal. Appl. 211 (1997) 1-29.
    • (1997) J. Math. Anal. Appl. , vol.211 , pp. 1-29
    • Scianna, G.1
  • 26
    • 0032097047 scopus 로고    scopus 로고
    • Morphological instability of similarity solution to the Stefan problem with kinetic undercooling and surface tension
    • I. Rubinstein and B. Zaltzman, Morphological instability of similarity solution to the Stefan problem with kinetic undercooling and surface tension, Quart. Appl. Math. 56 (1998) 341-354.
    • (1998) Quart. Appl. Math. , vol.56 , pp. 341-354
    • Rubinstein, I.1    Zaltzman, B.2
  • 27
    • 21144470884 scopus 로고
    • On a dissolution-growth problem with surface tension in the neighborhood of a stationary solution
    • F. Abergel, D. Hilhorst and F. Issard-Roch, On a dissolution-growth problem with surface tension in the neighborhood of a stationary solution, SIAM. J. Math. Anal. 24 (1993) 299-316.
    • (1993) SIAM. J. Math. Anal. , vol.24 , pp. 299-316
    • Abergel, F.1    Hilhorst, D.2    Issard-Roch, F.3
  • 28
    • 0012347002 scopus 로고
    • A dissolution-growth problem with surface tension: Local existence and uniqueness
    • J. F. Scheid, A dissolution-growth problem with surface tension: Local existence and uniqueness, Appl. Math. Lett. 8 (1995) 91-95.
    • (1995) Appl. Math. Lett. , vol.8 , pp. 91-95
    • Scheid, J.F.1
  • 29
    • 0000420079 scopus 로고
    • On a problem in the polymer industry: Theoretical and numerical investigation of swelling
    • A. Fasano, G. H. Meyer and M. Primicerio, On a problem in the polymer industry: Theoretical and numerical investigation of swelling, SIAM J. Math. Anal. 17 (1986) 945-960.
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 945-960
    • Fasano, A.1    Meyer, G.H.2    Primicerio, M.3
  • 30
    • 0023126064 scopus 로고
    • A free boundary problem arising from sorption of solvents in glassy polymers
    • D. Andreucci and R. Ricci, A free boundary problem arising from sorption of solvents in glassy polymers, Quart. Appl. Math. 19 (1987) 649-657.
    • (1987) Quart. Appl. Math. , vol.19 , pp. 649-657
    • Andreucci, D.1    Ricci, R.2
  • 31
    • 0012244384 scopus 로고
    • A free boundary value problem modeling thermal oxidation of silicon
    • K. Gröger and N. Strecker, A free boundary value problem modeling thermal oxidation of silicon, Zeit. Anal. Anwend. 7 (1988) 57-66.
    • (1988) Zeit. Anal. Anwend. , vol.7 , pp. 57-66
    • Gröger, K.1    Strecker, N.2
  • 32
    • 0001650810 scopus 로고
    • The Stefan problem with a kinetic condition at the free boundary
    • W. Xie, The Stefan problem with a kinetic condition at the free boundary, SIAM J. Math. Anal. 21 (1990) 362-373.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 362-373
    • Xie, W.1
  • 33
    • 0001304426 scopus 로고
    • Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling
    • X. Chen and F. Reitich, Local existence and uniqueness of solutions of 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
  • 34
    • 0012243710 scopus 로고
    • Interfacial kinetics effect in planar solidification problems without initial undercooling
    • Ch. Charach, B. Zaltzman, and I. G. Götz, Interfacial kinetics effect in planar solidification problems without initial undercooling, Math. Models Methods Appl. Sci. 4 (1994) 331-354.
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 331-354
    • Charach, Ch.1    Zaltzman, B.2    Götz, I.G.3
  • 35
    • 0642357473 scopus 로고
    • Two-phase Stefan problem with supercooling
    • I. G. Götz and B. Zaltzman, Two-phase Stefan problem with supercooling, SIAM J. Math. Anal. 26 (1995) 694-714.
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 694-714
    • Götz, I.G.1    Zaltzman, B.2
  • 36
    • 0001843626 scopus 로고
    • Stefan problem with a kinetic condition at the free boundary
    • A. Visintin, Stefan problem with a kinetic condition at the free boundary, Ann. Mat. Pura Appl. 146 (1987) 97-122.
    • (1987) Ann. Mat. Pura Appl. , vol.146 , pp. 97-122
    • Visintin, A.1
  • 37
    • 21344474063 scopus 로고    scopus 로고
    • Existence and blow-up of solutions to two-phase nonequilibrium problems
    • Z. Guan and X.-J. Wang, Existence and blow-up of solutions to two-phase nonequilibrium problems, SIAM J. Math. Anal. 27 (1996) 1038-1048.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1038-1048
    • Guan, Z.1    Wang, X.-J.2
  • 38
    • 0031510141 scopus 로고    scopus 로고
    • Critical exponent in a Stefan problem with kinetic condition
    • ____ and ____, Critical exponent in a Stefan problem with kinetic condition, Euro. J. Appl. Math. 8 (1997) 525-532.
    • (1997) Euro. J. Appl. Math. , vol.8 , pp. 525-532
    • Guan, Z.1    Wang, X.-J.2
  • 39
    • 0012248477 scopus 로고
    • Mathematical aspects of semiconductor process modelling
    • D.Phil. Thesis, Oxford University
    • J. R. King, Mathematical aspects of semiconductor process modelling, D.Phil. Thesis, Oxford University (1986).
    • (1986)
    • King, J.R.1
  • 40
    • 0012340842 scopus 로고
    • The isolation oxidation of silicon: The reaction-controlled case
    • ____, The isolation oxidation of silicon: The reaction-controlled case, SIAM J. Appl. Math. 49 (1989) 1064-1080.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1064-1080
    • King, J.R.1
  • 42
    • 0012343957 scopus 로고
    • Selective oxidation of silicon in low-temperature high-pressure steam
    • R. J. Powell, J. R. Ligenza and M. S. Schneider, Selective oxidation of silicon in low-temperature high-pressure steam, IEEE Trans. Electron Dev. ED 21 (1974) 636-640.
    • (1974) IEEE Trans. Electron Dev. ED , vol.21 , pp. 636-640
    • Powell, R.J.1    Ligenza, J.R.2    Schneider, M.S.3


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