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@article{M2AN_1999__33_4_797_0, author = {Imai, Hitoshi and Ishimura, Naoyuki and Ushijima, Takeo}, title = {Motion of spirals by crystalline curvature}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {797--806}, publisher = {EDP-Sciences}, volume = {33}, number = {4}, year = {1999}, mrnumber = {1726486}, zbl = {0944.34041}, language = {en}, url = {http://geodesic.mathdoc.fr/item/M2AN_1999__33_4_797_0/} }
TY - JOUR AU - Imai, Hitoshi AU - Ishimura, Naoyuki AU - Ushijima, Takeo TI - Motion of spirals by crystalline curvature JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 1999 SP - 797 EP - 806 VL - 33 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/M2AN_1999__33_4_797_0/ LA - en ID - M2AN_1999__33_4_797_0 ER -
%0 Journal Article %A Imai, Hitoshi %A Ishimura, Naoyuki %A Ushijima, Takeo %T Motion of spirals by crystalline curvature %J ESAIM: Mathematical Modelling and Numerical Analysis %D 1999 %P 797-806 %V 33 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/M2AN_1999__33_4_797_0/ %G en %F M2AN_1999__33_4_797_0
Imai, Hitoshi; Ishimura, Naoyuki; Ushijima, Takeo. Motion of spirals by crystalline curvature. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 33 (1999) no. 4, pp. 797-806. http://geodesic.mathdoc.fr/item/M2AN_1999__33_4_797_0/
[1] Crystalline Saffman-Taylor fingers. SIAM J. Appl. Math. 55 (1995) 1511-1535. | Zbl | MR
,[2] Multiphase thermodynamics with interfacial structure 2. Evolution of an isothermal interface. Arch. Rational Mech. Anal. 108 (1989) 323-391. | Zbl | MR
and ,[3] Crystalline curvature flow of a graph in a variational setting. Adv. Math. Sci. Appl. 8 (1998) 425-460. | Zbl | MR
, and ,[4] Motion of a graph by nonsmooth weighted curvature, in World Congress of Nonlinear Analysis '92, Vol. I, V. Lakshmikantham Ed., Walter de Gruyter, Berlin (1996) 47-56. | Zbl | MR
and ,[5] On the size of the blow-up set for a quasilinear parabolic equation. Contemp. Math. 127 (1992) 41-58. | Zbl | MR
,[6] Evolving graphs by singular weighted curvature, Arch. Rational Mech. Anal. 141 (1998) 117-198. | Zbl | MR
and ,[7] A comparison theorem for crystalline evolution in the plane. Quart. Appl Math. 54 (1996) 727-737. | Zbl | MR
and ,[8] On the dynamics of crystalline motion. Japan J. Indust, Appl. Math. 15 (1998) 7-50. | MR
, and ,[9] 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. | Zbl | MR
,[10] 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. | Zbl | MR
and ,[11] Thermomechanics of evolving phase boundaries in the plane. Oxford, Clarendon Press (1993). | Zbl | MR
,[12] On the structure of steady solutions for the kinematic model of spiral waves in excitable media. Japan J. Indust. Appl. Math. 15 (1998) 317-330. | Zbl | MR
, and ,[13] Regularity and convergence of crystalline motion. Preprint (1996). | Zbl | MR
and ,[14] Shape of spiral. Tôhoku Math. J. 50 (1998) 197-202. | Zbl | MR
,[15] A survey of spiral-wave behaviors in the oregonator model. Internat J, Bifur. Chaos 1 (1991). 445-466. | Zbl | MR
and ,[16] Kessyou ha ikiteiru (Crystal is alive). Science Sya, Tokyo (1984).
,[17] Complex dynamics of spiral waves and motion of curves. Pkysica D 70 (1994) 1-39. | Zbl | MR
, and ,[18] Kessyou seicyo (Crystal Growth). Syokabo, Tokyo (1977).
,[19] Modeling crystal growth in a diffusion field using fully faceted interfaces. J. Comput. Phys. 114 (1994) 113-128. | Zbl | MR
and ,[20] A quasi-steady approximation to an integro-differential model of interface motion. Appl Anal. 56 (1995) 19-34. | Zbl | MR
,[21] A crystalline motion: uniqueness and geometric properties. SIAM J. Appl. Math. 57 (1997) 53-72. | Zbl | MR
,[22] Observation and interpretation of eccentric growth spirals. J. Crystal Growth 42 (1977) 121-126.
, , and ,[23] Crystalline variational problem. Bull. Amer. Math. Soc. 84 (1978) 568-588. | Zbl | MR
,[24] Constructions and conjectures in crystalline nondifferential geometry, in Differential Geometry (A symposium in honour of Manfredo do Carmo) B, Lawson and K, Tenenblat Eds., Longman, Essex (1991) 321-336. | Zbl | MR
,[25] Motion of curves by crystalline curvature, including triple junctions and boundary points. Proc. Sympos. Pure. Math. 54 (1993) 417-438. | Zbl | MR
,[26] Surface motion due to crystalline surface energy gradient flows, in Elliptic and Parabolic Methods in Geometry, B. Chow, R. Gulliver, S. Levy, J. Sulliva and A.K. Peters Eds., Massachusetts (1996) 145-162. | Zbl | MR
,[27] Singular perturbation theory of traveling waves in excitable media. Physica D 32 (1988) 327-361. | Zbl | MR
and ,[28] Convergence of a crystalline algorithm for the motion of a closed convex curve by a power of curvature v = kα. Preprint (1997). | Zbl | MR
and ,