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Volumn 14, Issue 3, 2012, Pages 365-400

Uniqueness and existence of spirals moving by forced mean curvature motion

Author keywords

Comparison principle; Mean curvature motion; Motion of interfaces; Quasi linear parabolic equation; Spirals; Viscosity solutions

Indexed keywords


EID: 84872440640     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/285     Document Type: Article
Times cited : (6)

References (32)
  • 1
    • 84972538842 scopus 로고
    • Singularities of the curve shrinking flow for space curves
    • Zbl0754.53006 MR1131441
    • ALTSCHULER, S. J., Singularities of the curve shrinking flow for space curves, J. Differential Geom. 34 (1991), 491-514. Zbl0754.53006 MR1131441
    • (1991) J. Differential Geom , vol.34 , pp. 491-514
    • Altschuler, S.J.1
  • 2
    • 84972503988 scopus 로고
    • On the formation of singularities in the curve shortening flow
    • Zbl0731.53002 MR1100205
    • ANGENENT, S., On the formation of singularities in the curve shortening flow, J. Differential Geom. 33 (1991), 601-633. Zbl0731.53002 MR1100205
    • (1991) J. Differential Geom , vol.33 , pp. 601-633
    • Angenent, S.1
  • 3
    • 0007548518 scopus 로고
    • Asymptotic shape of cusp singularities in curve shortening
    • Zbl0829.35058 MR1317628
    • ANGENENT, S. B. & VEĹAZQUEZ, J. J. L., Asymptotic shape of cusp singularities in curve shortening, Duke Math. J. 77 (1995), 71-110. Zbl0829.35058 MR1317628
    • (1995) Duke Math. J , vol.77 , pp. 71-110
    • Angenent, S.B.1    Veĺazquez, J.J.L.2
  • 5
    • 0142168487 scopus 로고    scopus 로고
    • Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods
    • DOI 10.1007/s00526-002-0186-5
    • BARLES, G., BITON, S., BOURGOING, M., & LEY, O., Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods, Calc. Var. Partial Differential Equations 18 (2003), 159- 179. Zbl1036.35001 MR2010963 (Pubitemid 37316307)
    • (2003) Calculus of Variations and Partial Differential Equations , vol.18 , Issue.2 , pp. 159-179
    • Barles, G.1    Biton, S.2    Bourgoing, M.3    Ley, O.4
  • 6
    • 0000067621 scopus 로고
    • The growth crystals and the equilibrium structure of their surfaces
    • Zbl0043.23402 MR0043005
    • BURTON, W. K., CABRERA, N., & FRANK, F. C., The growth crystals and the equilibrium structure of their surfaces, Philos. Trans. Roy. Soc. London. Ser. A. 243 (1951), 299-358. Zbl0043.23402 MR0043005
    • (1951) Philos. Trans. Roy. Soc. London. Ser. A , vol.243 , pp. 299-358
    • Burton, W.K.1    Cabrera, N.2    Frank, F.C.3
  • 8
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Zbl0696.35087 MR1100211
    • CHEN, Y. G., GIGA, Y., & GOTO, S., Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33 (1991), 749-786. Zbl0696.35087 MR1100211
    • (1991) J. Differential Geom , vol.33 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 9
    • 0001588474 scopus 로고    scopus 로고
    • On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth
    • CHOU, K.-S., & KWONG, Y.-C., On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth, Calc. Var. 12 (2001), 281-315. Zbl0980.35061 MR1825875 (Pubitemid 33687549)
    • (2001) Calculus of Variations and Partial Differential Equations , vol.12 , Issue.3 , pp. 281-315
    • Chou, K.-S.1    Kwong, Y.-C.2
  • 10
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Zbl0755.35015 MR1118699
    • CRANDALL.M. G., ISHII, H., & LIONS, P.-L.,User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1-67. Zbl0755.35015 MR1118699
    • (1992) Bull. Amer. Math. Soc. (N.S) , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Ions, P.-L.3
  • 12
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature i
    • Zbl0726.53029 MR1100206
    • EVANS, L. C. & SPRUCK, J., Motion of level sets by mean curvature. I, J. Differential Geom. 33 (1991), 635-681. Zbl0726.53029 MR1100206
    • (1991) J. Differential Geom , Issue.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 15
    • 9544229550 scopus 로고    scopus 로고
    • Spiral solutions for a weakly anisotropic curvature flow equation
    • Zbl1038.35034 MR1909454
    • GIGA, Y., ISHIMURA, N., & KOHSAKA, Y., Spiral solutions for a weakly anisotropic curvature flow equation, Adv. Math. Sci. Appl. 12 (2002), 393-408. Zbl1038.35034 MR1909454
    • (2002) Adv. Math. Sci. Appl , vol.12 , pp. 393-408
    • Giga, Y.1    Ishimura, N.2    Kohsaka, Y.3
  • 16
    • 0001024159 scopus 로고
    • Generalized interface evolution with the Neumann boundary condition
    • Zbl0786.35076 MR1137924
    • GIGA, Y. & SATO, M.-H., Generalized interface evolution with the Neumann boundary condition, Proc. Japan Acad. Ser. A Math. Sci. 67 (1991), 263-266. Zbl0786.35076 MR1137924
    • (1991) Proc. Japan Acad. Ser. A Math. Sci , vol.67 , pp. 263-266
    • Giga, Y.1    Sato, M.-H.2
  • 17
    • 57449102826 scopus 로고    scopus 로고
    • Uniqueness and existence of generalized motion for spiral crystal growth
    • Zbl1161.53057 MR2463977
    • GOTO, S., NAKAGAWA, M., & OHTSUKA, T., Uniqueness and existence of generalized motion for spiral crystal growth, Indiana Univ. Math. J. 57 (2008), 2571-2599. Zbl1161.53057 MR2463977
    • (2008) Indiana Univ. Math. J , vol.57 , pp. 2571-2599
    • Goto, S.1    Nakagawa, M.2    Ohtsuka, T.3
  • 18
    • 84972566521 scopus 로고
    • Perron's method for Hamilton-Jacobi equations
    • Zbl069735030 MR0894587
    • ISHII, H., Perron's method for Hamilton-Jacobi equations, Duke Math. J. (2) 55 (1987), 369-384. Zbl0697.35030 MR0894587
    • (1987) Duke Math. J. , vol.2 , Issue.55 , pp. 369-384
    • Ishii, H.1
  • 19
    • 0032378271 scopus 로고    scopus 로고
    • Shape of spirals
    • Zbl091535048 MR1622050
    • ISHIMURA, N., Shape of spirals, Tohoku Math. J. (2) 50 (1998), 197-202. Zbl0915.35048 MR1622050
    • (1998) Tohoku Math. J. , vol.2 , Issue.50 , pp. 197-202
    • Ishimura, N.1
  • 20
    • 0001001797 scopus 로고    scopus 로고
    • Spiral surface growth without desorption
    • KARMA, A. & PLAPP, M., Spiral surface growth without desorption, Physical Review Letters 81 (1998), 4444-4447. http://dx.doi.org/10.1103/ PhysRevLett.81.4444. (Pubitemid 128630834)
    • (1998) Physical Review Letters , vol.81 , Issue.20 , pp. 4444-4447
    • Karma, A.1    Plapp, M.2
  • 21
    • 0003919106 scopus 로고    scopus 로고
    • of Interdisciplinary Applied Mathematics, Springer- Verlag, New York. Zbl0913.92009 MR1673204
    • KEENER, J. & SNEYD, J., Mathematical physiology, vol. 8 of Interdisciplinary Applied Mathematics, Springer-Verlag, New York, 1998. Zbl0913.92009 MR1673204
    • (1998) Mathematical Physiology , vol.8
    • Keener, J.1    Sneyd, J.2
  • 22
    • 84872450883 scopus 로고
    • Translated from the Russian by S. Smith. Translations of Mathematical Monographs American Mathematical Society, Providence, R.I. Zbl0164.12302 MR0241822
    • LADYZ ENSKAJA, O. A., SOLONNIKOV, V. A., & URAL0CEVA, N. N., Linear and quasilinear equations of parabolic type, Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, R.I., (1967). Zbl0164.12302 MR0241822
    • (1967) Linear and Quasilinear Equations of Parabolic Type , vol.23
    • Ladyz Enskaja, O.A.1    Solonnikov, V.A.2    Uraloceva, N.N.3
  • 23
    • 84863995308 scopus 로고    scopus 로고
    • Homogenization of the Peierls-Nabarro model for dislocation dynamics
    • Zblre06071615 MR2946964
    • MONNEAU, R. & PATRIZI, S., Homogenization of the Peierls-Nabarro model for dislocation dynamics, J. Differ Equations 253, 2064-2105 (2012). Zblpre06071615 MR2946964
    • (2012) J. Differ Equations , vol.253 , pp. 2064-2105
    • Monneau, R.1    Patrizi, S.2
  • 25
    • 0003475470 scopus 로고    scopus 로고
    • of Biomathematics, Springer- Verlag, Berlin, Zbl0779. 92001 MR1239892
    • MURRAY, J. D., Mathematical biology, vol. 19 of Biomathematics, Springer-Verlag, Berlin, Zbl0779. 92001 MR1239892
    • Mathematical Biology , vol.19
    • Murray, J.D.1
  • 26
    • 1942507733 scopus 로고    scopus 로고
    • Spiral traveling wave solutions of some parabolic equations on annuli
    • of Josai Math. Monogr., Josai Univ., Sakado Zbl096235100 MR1761978
    • OGIWARA, T. & NAKAMURA, K.-I., Spiral traveling wave solutions of some parabolic equations on annuli, in NLA99: Computer algebra (Saitama, 1999), vol. 2 of Josai Math. Monogr., Josai Univ., Sakado, 2000, 15-34. Zbl0962.35100 MR1761978
    • NLA99: Computer Algebra (Saitama 1999) , vol.2 , Issue.2000 , pp. 15-34
    • Ogiwara, T.1    Nakamura, K.-I.2
  • 27
    • 1942536643 scopus 로고    scopus 로고
    • Spiral Traveling Wave Solutions of Nonlinear Diffusion Equations Related to a Model of Spiral Crystal Growth
    • OGIWARA, T. & NAKAMURA, K.-I., Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral crystal growth, Publ. Res. Inst. Math. Sci. 39 (2003), 767-783. Zbl1056. 35026 MR2025462 (Pubitemid 38516682)
    • (2003) Publications of the Research Institute for Mathematical Sciences , vol.39 , Issue.4 , pp. 767-783
    • Ogiwara, T.1    Nakamura, K.-I.2
  • 28
    • 38049154294 scopus 로고    scopus 로고
    • A level set method for spiral crystal growth
    • Zbl1059.74045 MR2002402
    • OHTSUKA, T., A level set method for spiral crystal growth, Adv. Math. Sci. Appl. 13 (2003), 225-248. Zbl1059.74045 MR2002402
    • (2003) Adv. Math. Sci. Appl , vol.13 , pp. 225-248
    • Ohtsuka, T.1
  • 29
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations
    • Zbl0659.65132 MR0965860
    • OSHER, S. & SETHIAN, J. A., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79 (1988), 12-49. Zbl0659.65132 MR0965860
    • (1988) J. Comput. Phys , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 30
    • 0000114118 scopus 로고
    • Interface evolution with Neumann boundary condition
    • Zbl0811.35069 MR1287918
    • SATO, M.-H., Interface evolution with Neumann boundary condition, Adv. Math. Sci. Appl. 4 (1994), 249-264. Zbl0811.35069 MR1287918
    • (1994) Adv. Math. Sci. Appl , vol.4 , pp. 249-264
    • Sato, M.-H.1
  • 31
    • 0039765174 scopus 로고    scopus 로고
    • A geometric model for coarsening during spiral-mode growth of thin films
    • Zbl0962.74522 MR1704821
    • SCHULZE, T. P. & KOHN, R. V., A geometric model for coarsening during spiral-mode growth of thin films, Phys. D 132 (1999), 520-542. Zbl0962.74522 MR1704821
    • (1999) Phys D 132 , pp. 520-542
    • Schulze, T.P.1    Kohn, R.V.2
  • 32
    • 0346819812 scopus 로고    scopus 로고
    • Spiral crystal growth
    • Zbl0957.80002 MR1744632
    • SMEREKA, P., Spiral crystal growth, Phys. D 138 (2000), 282-301. Zbl0957.80002 MR1744632
    • (2000) Phys D 138 , pp. 282-301
    • Smereka, P.1


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