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Spiral rotating waves of a geodesic curvature flow on the unit sphere
1. | Department of Mathematics, Tongji University, Shanghai 200092 |
References:
[1] |
M. Alfaro, D. Hilhorst and H. Matano, The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system, J. Differential Equations, 245 (2008), 505-565.
doi: 10.1016/j.jde.2008.01.014. |
[2] |
S. J. Altschuler, Singularities of the curve shrinking flow for space curves, J. Differential Geom., 34 (1991), 491-514. |
[3] |
F. Amdjadi and J. Gomatam, Spiral waves on static and moving spherical domains, J. Comput. Appl. Math., 182 (2005), 472-486.
doi: 10.1016/j.cam.2004.12.027. |
[4] |
X. Chen, Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations, 96 (1992), 116-141.
doi: 10.1016/0022-0396(92)90146-E. |
[5] |
K.-S. Chou and X.-P. Zhu, "The Curve Shorting Problem," Chapman & Hall/CRC, Boca Raton, FL, 2001.
doi: 10.1201/9781420035704. |
[6] |
P. C. Fife, "Dynamics of Internal Layers and Diffusive Interfaces," CBMS-NSF Regional Conference Series in Applied Mathematics, 53, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988. |
[7] |
J. Gomatam and F. Amdjadi, Reaction-diffusion equations on a sphere: Meandering of spiral waves, Physical Review E (3), 56 (1997), 3913-3919. |
[8] |
R. Ikota, N. Ishimura and T. Yamaguchi, 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.
doi: 10.1007/BF03167407. |
[9] |
J. P. Keener, The core of the spiral, SIAM J. Appl. Math., 52 (1992), 1370-1390.
doi: 10.1137/0152079. |
[10] |
J. P. Keener and J. J. Tyson, Spiral waves in the Belousov-Zhabotinski reaction, Phys. D, 21 (1986), 307-324.
doi: 10.1016/0167-2789(86)90007-2. |
[11] |
B. Lou, Periodic rotating waves of a geodesic curvature flow on the sphere, Commun. Partial Differential Equations, 32 (2007), 525-541.
doi: 10.1080/03605300701249663. |
[12] |
B. D. Lou and L. Zhou, Singular limit of FitzHugh-Nagumo equations on a sphere, ZAMM Z. Angew. Math. Mech., 88 (2008), 644-649.
doi: 10.1002/zamm.200700144. |
[13] |
H. Matano, K.-I. Nakamura and B. Lou, Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit, Netw. Heterog. Media, 1 (2006), 537-568.
doi: 10.3934/nhm.2006.1.537. |
[14] |
K.-I. Nakamura, H. Matano, D. Hilhorst and R. Schätzle, Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term, J. Statist. Phys., 95 (1999), 1165-1185.
doi: 10.1023/A:1004518904533. |
[15] |
T. Ogiwara and K.-I. Nakamura, 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.
doi: 10.2977/prims/1145476046. |
show all references
References:
[1] |
M. Alfaro, D. Hilhorst and H. Matano, The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system, J. Differential Equations, 245 (2008), 505-565.
doi: 10.1016/j.jde.2008.01.014. |
[2] |
S. J. Altschuler, Singularities of the curve shrinking flow for space curves, J. Differential Geom., 34 (1991), 491-514. |
[3] |
F. Amdjadi and J. Gomatam, Spiral waves on static and moving spherical domains, J. Comput. Appl. Math., 182 (2005), 472-486.
doi: 10.1016/j.cam.2004.12.027. |
[4] |
X. Chen, Generation and propagation of interfaces for reaction-diffusion equations, J. Differential Equations, 96 (1992), 116-141.
doi: 10.1016/0022-0396(92)90146-E. |
[5] |
K.-S. Chou and X.-P. Zhu, "The Curve Shorting Problem," Chapman & Hall/CRC, Boca Raton, FL, 2001.
doi: 10.1201/9781420035704. |
[6] |
P. C. Fife, "Dynamics of Internal Layers and Diffusive Interfaces," CBMS-NSF Regional Conference Series in Applied Mathematics, 53, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988. |
[7] |
J. Gomatam and F. Amdjadi, Reaction-diffusion equations on a sphere: Meandering of spiral waves, Physical Review E (3), 56 (1997), 3913-3919. |
[8] |
R. Ikota, N. Ishimura and T. Yamaguchi, 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.
doi: 10.1007/BF03167407. |
[9] |
J. P. Keener, The core of the spiral, SIAM J. Appl. Math., 52 (1992), 1370-1390.
doi: 10.1137/0152079. |
[10] |
J. P. Keener and J. J. Tyson, Spiral waves in the Belousov-Zhabotinski reaction, Phys. D, 21 (1986), 307-324.
doi: 10.1016/0167-2789(86)90007-2. |
[11] |
B. Lou, Periodic rotating waves of a geodesic curvature flow on the sphere, Commun. Partial Differential Equations, 32 (2007), 525-541.
doi: 10.1080/03605300701249663. |
[12] |
B. D. Lou and L. Zhou, Singular limit of FitzHugh-Nagumo equations on a sphere, ZAMM Z. Angew. Math. Mech., 88 (2008), 644-649.
doi: 10.1002/zamm.200700144. |
[13] |
H. Matano, K.-I. Nakamura and B. Lou, Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit, Netw. Heterog. Media, 1 (2006), 537-568.
doi: 10.3934/nhm.2006.1.537. |
[14] |
K.-I. Nakamura, H. Matano, D. Hilhorst and R. Schätzle, Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term, J. Statist. Phys., 95 (1999), 1165-1185.
doi: 10.1023/A:1004518904533. |
[15] |
T. Ogiwara and K.-I. Nakamura, 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.
doi: 10.2977/prims/1145476046. |
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