메뉴 건너뛰기




Volumn 18, Issue 8, 2008, Pages 1347-1381

Allen-Cahn systems with volume constraints

Author keywords

Finite differences; Phase field; Semi smooth Newton method

Indexed keywords

CHLORINE COMPOUNDS; COMPUTER NETWORKS; EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; GRADIENT METHODS; NUMERICAL ANALYSIS; SURFACE CHEMISTRY; SURFACE TENSION;

EID: 50949128255     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202508003066     Document Type: Article
Times cited : (51)

References (21)
  • 1
    • 50949118850 scopus 로고    scopus 로고
    • J. F. Blowey and C. M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, Degenerate diffusions (Minneapolis, 1991), IMA Math. Appl. 47 (1993) 19-60.
    • J. F. Blowey and C. M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, Degenerate diffusions (Minneapolis, 1991), IMA Vol. Math. Appl. 47 (1993) 19-60.
  • 2
    • 11744273384 scopus 로고
    • The surface evolver
    • K. A. Brakke, The surface evolver, Experiment. Math. 1 (1992) 141-165.
    • (1992) Experiment. Math , vol.1 , pp. 141-165
    • Brakke, K.A.1
  • 3
    • 0031484192 scopus 로고    scopus 로고
    • Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg - Landau equation
    • L. Bronsard and B. Stoth, Volume-preserving mean curvature flow as a limit of a nonlocal Ginzburg - Landau equation, SIAM J. Math. Anal. 28 (1997) 769-807.
    • (1997) SIAM J. Math. Anal , vol.28 , pp. 769-807
    • Bronsard, L.1    Stoth, B.2
  • 4
    • 0000381088 scopus 로고
    • Shape evolution by diffusion and surface attachment limited kinetics on completely faceted surfaces
    • C. Carter, A. Roosen, J. Cahn and J. E. Taylor, Shape evolution by diffusion and surface attachment limited kinetics on completely faceted surfaces, Acta Metal. Mater. 43 (1995) 4309-4323.
    • (1995) Acta Metal. Mater , vol.43 , pp. 4309-4323
    • Carter, C.1    Roosen, A.2    Cahn, J.3    Taylor, J.E.4
  • 5
    • 85120508144 scopus 로고    scopus 로고
    • Finite elements on evolving surfaces
    • doi:10.1093/imanum/dr1023
    • G. Dziuk and C. M. Elliott, Finite elements on evolving surfaces, IMA J. Numer. Anal. doi:10.1093/imanum/dr1023.
    • IMA J. Numer. Anal
    • Dziuk, G.1    Elliott, C.M.2
  • 7
    • 84891542607 scopus 로고    scopus 로고
    • On Ginzburg - Landau type free energies for multiphase systems
    • in preparation
    • H. Garcke, R. Haas and B. Stinner, On Ginzburg - Landau type free energies for multiphase systems, in preparation.
    • Garcke, H.1    Haas, R.2    Stinner, B.3
  • 8
    • 0003112331 scopus 로고    scopus 로고
    • On anisotropic order parameter models for multiphase systems and their sharp interface limits
    • H. Garcke, B. Nestler and B. Stoth, On anisotropic order parameter models for multiphase systems and their sharp interface limits, Physica D 115 (1998) 87-108.
    • (1998) Physica D , vol.115 , pp. 87-108
    • Garcke, H.1    Nestler, B.2    Stoth, B.3
  • 9
    • 84992261084 scopus 로고    scopus 로고
    • Anisotropy in multiphase systems: A phase-field approach
    • H. Garcke, B. Nestler and B. Stoth, Anisotropy in multiphase systems: A phase-field approach, Interfaces and Free Boundaries 1 (1999) 175-198.
    • (1999) Interfaces and Free Boundaries , vol.1 , pp. 175-198
    • Garcke, H.1    Nestler, B.2    Stoth, B.3
  • 10
    • 0034398259 scopus 로고    scopus 로고
    • A mathematical model for grain growth in thin metallic films
    • H. Garcke and B. Nestler, A mathematical model for grain growth in thin metallic films, Math. Mod. Meth. Appl. Sci. 10 (2000) 895-921.
    • (2000) Math. Mod. Meth. Appl. Sci , vol.10 , pp. 895-921
    • Garcke, H.1    Nestler, B.2
  • 11
    • 33751016022 scopus 로고    scopus 로고
    • Surfactant spreading on thin viscous films: Nonnegative solutions of a coupled degenerate system
    • H. Garcke and S. Wieland, Surfactant spreading on thin viscous films: Nonnegative solutions of a coupled degenerate system, SIAM J. Math. Anal. 37 (2006) 2025-2048.
    • (2006) SIAM J. Math. Anal , vol.37 , pp. 2025-2048
    • Garcke, H.1    Wieland, S.2
  • 14
    • 50949095410 scopus 로고    scopus 로고
    • Geometric measure theory and the proof of the double bubble conjecture, Global theory of minimal surfaces
    • Amer. Math. Soc
    • F. Morgan and M. Ritoré, Geometric measure theory and the proof of the double bubble conjecture, Global theory of minimal surfaces, in Clay Math. Proc., Vol. 2 (Amer. Math. Soc., 2005) pp. 1-18.
    • (2005) Clay Math. Proc , vol.2 , pp. 1-18
    • Morgan, F.1    Ritoré, M.2
  • 15
    • 0027543961 scopus 로고
    • A nonsmooth version of Newton's method
    • L. Qi and J. Sun, A nonsmooth version of Newton's method, Math. Program. 58 (1993) 353-367.
    • (1993) Math. Program , vol.58 , pp. 353-367
    • Qi, L.1    Sun, J.2
  • 16
    • 77958411749 scopus 로고
    • Nonlocal reaction-diffusion equations and nucleation
    • J. Rubinstein and P. Sternberg, Nonlocal reaction-diffusion equations and nucleation, IMA J. Appl. Math. 48 (1992) 249-264.
    • (1992) IMA J. Appl. Math , vol.48 , pp. 249-264
    • Rubinstein, J.1    Sternberg, P.2
  • 17
    • 0026899706 scopus 로고
    • Mean curvature and weighted mean curvature
    • J. E. Taylor, Mean curvature and weighted mean curvature, Acta Metall. Mater. 40 (1992) 1475-1485.
    • (1992) Acta Metall. Mater , vol.40 , pp. 1475-1485
    • Taylor, J.E.1
  • 18
    • 0000685099 scopus 로고
    • On the division of space with minimum partitional area
    • W. Thomson, On the division of space with minimum partitional area, Phil. Mag. 24 (1887) 503.
    • (1887) Phil. Mag , vol.24 , pp. 503
    • Thomson, W.1
  • 19
    • 84966231127 scopus 로고
    • What the bees know and what they do not know
    • L. Fejes Tóth, What the bees know and what they do not know, Bull. Amer. Math. Soc. 70 (1964) 468-481.
    • (1964) Bull. Amer. Math. Soc , vol.70 , pp. 468-481
    • Fejes Tóth, L.1
  • 20
    • 50949092604 scopus 로고    scopus 로고
    • D. Weaire and R. Phelan, A counter-example to Kelvin's conjecture on minimal surfaces, Forma 11 (1996) 209-213, reprint of Philos. Mag. Lett. 69 (1994) 107-110.
    • D. Weaire and R. Phelan, A counter-example to Kelvin's conjecture on minimal surfaces, Forma 11 (1996) 209-213, reprint of Philos. Mag. Lett. 69 (1994) 107-110.
  • 21
    • 0030269055 scopus 로고    scopus 로고
    • Metastable bubble solutions for the Allen - Cahn equation with mass conservation
    • M. J. Ward, Metastable bubble solutions for the Allen - Cahn equation with mass conservation, SIAM J. Appl. Math. 56 (1996) 1247-1279.
    • (1996) SIAM J. Appl. Math , vol.56 , pp. 1247-1279
    • Ward, M.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.