@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {33}, year = {1999}, pages = {797-806}, mrnumber = {1726486}, zbl = {0944.34041}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1999__33_4_797_0} }
Imai, Hitoshi; Ishimura, Naoyuki; Ushijima, Takeo. Motion of spirals by crystalline curvature. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 797-806. http://gdmltest.u-ga.fr/item/M2AN_1999__33_4_797_0/
[1] Crystalline Saffman-Taylor fingers. SIAM J. Appl. Math. 55 (1995) 1511-1535. | MR 1358787 | Zbl 0838.76094
,[2] Multiphase thermodynamics with interfacial structure 2. Evolution of an isothermal interface. Arch. Rational Mech. Anal. 108 (1989) 323-391. | MR 1013461 | Zbl 0723.73017
and ,[3] Crystalline curvature flow of a graph in a variational setting. Adv. Math. Sci. Appl. 8 (1998) 425-460. | MR 1623315 | Zbl 0959.35168
, 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. | MR 1389060 | Zbl 0860.35061
and ,[5] On the size of the blow-up set for a quasilinear parabolic equation. Contemp. Math. 127 (1992) 41-58. | MR 1155408 | Zbl 0770.35029
,[6] Evolving graphs by singular weighted curvature, Arch. Rational Mech. Anal. 141 (1998) 117-198. | MR 1615520 | Zbl 0896.35069
and ,[7] A comparison theorem for crystalline evolution in the plane. Quart. Appl Math. 54 (1996) 727-737. | MR 1417236 | Zbl 0862.35047
and ,[8] On the dynamics of crystalline motion. Japan J. Indust, Appl. Math. 15 (1998) 7-50. | MR 1610305
, 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. | MR 1335660 | Zbl 0830.65150
,[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. | MR 1258974 | Zbl 0791.65063
and ,[11] Thermomechanics of evolving phase boundaries in the plane. Oxford, Clarendon Press (1993). | MR 1402243 | Zbl 0787.73004
,[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. | MR 1629103 | Zbl 0904.92002
, and ,[13] Regularity and convergence of crystalline motion. Preprint (1996). | MR 1646732 | Zbl 0963.35082
and ,[14] Shape of spiral. Tôhoku Math. J. 50 (1998) 197-202. | MR 1622050 | Zbl 0915.35048
,[15] A survey of spiral-wave behaviors in the oregonator model. Internat J, Bifur. Chaos 1 (1991). 445-466. | MR 1120210 | Zbl 0900.92066
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. | MR 1257848 | Zbl 0807.58043
, 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. | MR 1286190 | Zbl 0805.65128
and ,[20] A quasi-steady approximation to an integro-differential model of interface motion. Appl Anal. 56 (1995) 19-34. | MR 1378009 | Zbl 0832.35155
,[21] A crystalline motion: uniqueness and geometric properties. SIAM J. Appl. Math. 57 (1997) 53-72. | MR 1429377 | Zbl 0870.35129
,[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. | MR 493671 | Zbl 0392.49022
,[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. | MR 1173051 | Zbl 0725.53011
,[25] Motion of curves by crystalline curvature, including triple junctions and boundary points. Proc. Sympos. Pure. Math. 54 (1993) 417-438. | MR 1216599 | Zbl 0823.49028
,[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. | MR 1417953 | Zbl 0915.49024
,[27] Singular perturbation theory of traveling waves in excitable media. Physica D 32 (1988) 327-361. | MR 980194 | Zbl 0656.76018
and ,[28] Convergence of a crystalline algorithm for the motion of a closed convex curve by a power of curvature v = kα. Preprint (1997). | MR 1740769 | Zbl 0946.65071
and ,