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CRYSTALLINE FLOW STARTING FROM A GENERAL POLYGON

Giga, Mi-Ho Giga, Yoshikazu Kuroda, Ryo Ochiai, Yusuke 北海道大学

2021.03.04

概要

This paper solves a singular initial value problem for a system of ordinary di erential equations describing a polygonal flow called a crystalline flow. Such a problem corresponds to a crystalline flow starting from a general polygon not necessarily admissible in the sense that the corresponding initial value problem is singular. To solve the problem, a self-similar expanding solution constructed by the first two authors with H. Hontani (2006) is effectively used.

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参考文献

[A] B. Andrews, Singularities in crystalline curvature flows, Asian J. Math., 6 (2002), 101– 121.

[AG] S. Angenent and M. E. Gurtin, Multiphase thermomechanics with interfacial structure. II. Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108 (1989), 323– 391.

[BNP1] G. Bellettini, M. Novaga and M. Paolini, Facet-breaking for three-dimensional crystals evolving by mean curvature, Interfaces Free Bound., 1 (1999), 39–55.

[BNP2] G. Bellettini, M. Novaga and M. Paolini, Characterization of facet breaking for non- smooth mean curvature flow in the convex case, Interfaces Free Bound., 3 (2001), 415–446.

[Ca] D. Campbell, A first glance at crystal motion, Master’s thesis, Rutgers University, New Brunswick, NJ, 2002.

[CMMP] A. Chambolle, M. Morini, M. Novaga and M. Ponsiglione, Existence and uniqueness for anisotropic and crystalline mean curvature flows, J. Amer. Math. Soc., 32 (2019), 779–824.

[CMP] A. Chambolle, M. Morini and M. Ponsiglione, Existence and uniqueness for a crystalline mean curvature flow, Comm. Pure Appl. Math., 70 (2017), 1084–1114.

[CGG] Y. G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom., 33 (1991), 749–786.

[DG] C. Dohmen and Y. Giga, Selfsimilar shrinking curves for anisotropic curvature flow equations, Proc. Japan Acad. Ser. A Math. Sci., 70 (1994), 252–255.

[DGM] C. Dohmen, Y. Giga and N. Mizoguchi, Existence of selfsimilar shrinking curves for anisotropic curvature flow equations, Calc. Var. Partial Differential Equations, 4 (1996), 103–119.

[EGS] C. M. Elliott, A. R. Gardiner and R. Sch¨atzle, Crystalline curvature flow of a graph in a variational setting, Adv. Math. Sci. Appl., 8 (1998), 425–460.

[ES] L. C. Evans and J. Spruck, Motion of level sets by mean curvature, I. J. Differential Geom., 33 (1991), 635–681.

[FG] T. Fukui and Y. Giga, Motion of a graph by nonsmooth weighted curvature, in World Congress of Nonlinear Analysts ’92, Vol. I–IV (Tampa, FL, 1992), 47–56, de Gruyter, Berlin, 1996.

[Ga93] M. E. Gage, Evolving plane curves by curvature in relative geometries, Duke Math. J., 72 (1993), 441–466.

[GaL94] M. E. Gage and Y. Li, Evolving plane curves by curvature in relative geometries. II, Duke Math. J., 75 (1994), 79–98.

[GeT] R. G´erard and H. Tahara, Singular nonlinear partial differential equations. Aspects of Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1996.

[GG96] M.-H. Giga and Y. Giga, Consistency in evolutions by crystalline curvature, Free bound- ary problems, theory and applications (Zakopane, 1995), 186–202, Pitman Res. Notes Math. Ser., 363, Longman, Harlow, 1996.

[GG] M.-H. Giga and Y. Giga, Geometric evolution by nonsmooth interfacial energy, Nonlin- ear analysis and applications (Warsaw, 1994), 125–140, GAKUTO Internat. Ser. Math. Sci. Appl., 7, Gakk¯otosho, Tokyo, 1996.

[GG98] M.-H. Giga and Y. Giga, A subdifferential interpretation of crystalline motion under nonuniform driving force, Dynamical systems and differential equations, Vol. I (Spring- field, MO, 1996). Discrete Contin. Dynam. Systems 1998, Added Volume I, 276–287.

[GG1] M.-H. Giga and Y. Giga, Evolving graphs by singular weighted curvature, Arch. Ratio- nal Mech. Anal., 141 (1998), 117–198.

[GG2] M.-H. Giga and Y. Giga, Stability for evolving graphs by nonlocal weighted curvature, Comm. Partial Differential Equations, 24 (1999), 109–184.

[GG3] M.-H. Giga and Y. Giga, Crystalline and level set flow – convergence of a crystalline algorithm for a general anisotropic curvature flow in the plane, Free boundary problems: theory and applications, I (Chiba, 1999), 64–79, GAKUTO Internat. Ser. Math. Sci. Appl., 13, Gakk¯otosho, Tokyo, 2000.

[GG4] M.-H. Giga and Y. Giga, Generalized motion by nonlocal curvature in the plane, Arch. Ration. Mech. Anal., 159 (2001), 295–333.

[GG13] M.-H. Giga and Y. Giga, On the role of kinetic and interfacial anisotropy in the crystal growth theory, Interfaces Free Bound., 15 (2013), 429–450.

[GGH] M.-H. Giga, Y. Giga and H. Hontani, Self-similar expanding solutions in a sector for a crystalline flow, SIAM J. Math. Anal., 37 (2005), 1207–1226.

[GHK] Y. Giga, Motion of a graph by convexified energy, Hokkaido Math. J., 23 (1994), 185–212.

[G] Y. Giga, Surface evolution equations. A level set approach, Monographs in Mathematics, 99, Birkh¨auser Verlag, Basel, 2006.

[GGu] Y. Giga and M. E. Gurtin, A comparison theorem for crystalline evolution in the plane, Quart. Appl. Math., 54 (1996), 727–737.

[GP1] Y. Giga and N. Poˇz´ar, A level set crystalline mean curvature flow of surfaces, Adv. Differential Equations, 21 (2016), 631–698.

[GP2] Y. Giga and N. Poˇz´ar, Approximation of general facets by regular facets with respect to anisotropic total variation energies and its application to crystalline mean curvature flow, Comm. Pure Appl. Math., 71 (2018), 1461–1491.

[GP3] Y. Giga and N. Poˇz´ar, Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term, SN Partial Differ. Equ. Appl., 1 (2020), Article number: 39.

[Gir] P. M. Gir˜ao, Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature, SIAM J. Numer. Anal., 32 (1995), 886–899.

[GirK] P. M. Gir˜ao and R. V. Kohn, Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature, Numer. Math., 67 (1994), 41–70.

[Gr] M. A. Grayson, The heat equation shrinks embedded plane curves to round points. J. Differential Geom., 26 (1987), 285–314.

[Gu] M. E. Gurtin, Thermomechanics of evolving phase boundaries in the plane, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993.

[GSS] M. E. Gurtin, H. M. Soner and P. E. Souganidis, Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles, J. Differential Equations, 119 (1995), 54–108.

[IS] K. Ishii and H. M. Soner, Regularity and convergence of crystalline motion, SIAM J. Math. Anal., 30 (1999), 19–37.

[IJ] T. Ishiwata, Crystalline undou ni tsuite: heimenjou no takakukei no undou no kaiseki (Japanese) [On crystalline motion: analysis on motion of a polygon in the plane], Lecture Series in Mathematics GP-TML06, Graduate School of Science, Tohoku University, 2008.

[I08] T. Ishiwata, Motion of non-convex polygons by crystalline curvature and almost con- vexity phenomena, Japan J. Indust. Appl. Math., 25 (2008), 233–253.

[I11a] T. Ishiwata, Motion of polygonal curved fronts by crystalline motion: V-shaped solu- tions and eventual monotonicity, Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications. 8th AIMS Conference. Suppl. Vol. I, 717–726.

[I11b] T. Ishiwata, On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect, Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), 865–873.

[I14] T. Ishiwata, Crystalline motion of spiral-shaped polygonal curves with a tip motion, Discrete Contin. Dyn. Syst. Ser. S, 7 (2014), no. 1, 53–62.

[IO1] T. Ishiwata and T. Ohtsuka, Evolution of a spiral-shaped polygonal curve by the crys- talline curvature flow with a pinned tip, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 5261–5295.

[IO2] T. Ishiwata and T. Ohtsuka, Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow, Discrete Contin. Dyn. Syst. Ser. S, 14 (2021), 893–907.

[IUYY] T. Ishiwata, T. K. Ushijima, H. Yagisita and S. Yazaki, Two examples of nonconvex self-similar solution curves for a crystalline curvature flow, Proc. Japan Acad. Ser. A Math. Sci., 80 (2004), 151–154.

[K] R. Kuroda, Facet-creation between two facets moved by crystalline flow or similar equa- tions, Bachelor’s thesis, The University of Tokyo, Tokyo, 2019.

[Mu] P. B. Mucha, Regular solutions to a monodimensional model with discontinuous elliptic operator, Interfaces Free Bound., 14 (2012), 145–152.

[MuR1] P. B. Mucha and P. Rybka, A note on a model system with sudden directional diffusion, J. Stat. Phys., 146 (2012), 975–988.

[MuR2] P. B. Mucha and P. Rybka, Well posedness of sudden directional diffusion equations, Math. Methods Appl. Sci., 36 (2013), 2359–2370.

[OOTT] A. Oberman, S. Osher, R. Takei and R. Tsai, Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation, Commun. Math. Sci., 9 (2011), 637–662.

[O] Y. Ochiai, Facet-creation between two facets moved by crystalline curvature, Master’s thesis, The University of Tokyo, Tokyo, 2009.

[S1] A. Stancu, Uniqueness of self-similar solutions for a crystalline flow, Indiana Univ. Math. J., 45 (1996), 1157–1174.

[S2] A. Stancu, Asymptotic behavior of solutions to a crystalline flow. Hokkaido Math. J., 27 (1998), 303–320.

[T1] J. E. Taylor, Constructions and conjectures in crystalline nondifferential geometry, Dif- ferential geometry, 321–336, Pitman Monogr. Surveys Pure Appl. Math., 52, Longman Sci. Tech., Harlow, 1991.

[T2] J. E. Taylor, Mean curvature and weighted mean curvature, Acta Metall. Mater., 40 (1992), 1475–1485.

[T3] J. E. Taylor, Motion of curves by crystalline curvature, including triple junctions and boundary points, Differential geometry: partial differential equations on manifolds (Los Angeles, CA, 1990), 417–438, Proc. Sympos. Pure Math., 54, Part 1, Amer. Math. Soc., Providence, RI, 1993.

[Ya] S. Yazaki, Motion of nonadmissible convex polygons by crystalline curvature, Publ. Res. Inst. Math. Sci., 43 (2007), 155–170.

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