Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T06:46:33.632Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of solutions for equations related to the motions of plane curves

Published online by Cambridge University Press:  17 February 2009

Jong-Shenq Guo ,
Chu-Pin Lo  and
Je-Chiang Tsai
Jong-Shenq Guo
Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, S-4 Ting Chou Road, Taipei 117, Taiwan.
Chu-Pin Lo
Affiliation:
Department of Finance and Taxation, Dahan Institute of Technology, I, Sujen Street, Dahan, Sincheng, Hualian 971, Taiwan.
Je-Chiang Tsai
Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, S-4 Ting Chou Road, Taipei 117, Taiwan.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the structure of solutions of an initial value problem arising in the study of steadily rotating spiral waves in the kinematic theory of excitable media. In particular, we prove that under certain conditions there is a unique global positive monotone increasing solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 585 - 592
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Brazhnik, P. K., “Exact solutions for the kinematic model of autowaves in two-dimensional excitable media”, Physica D 94 (1996) 205–220.CrossRefGoogle Scholar
[2]Giga, Y., Ishimura, N. and Kohsaka, Y., “Spiral solutions for a weakly anisotropic curvature flow equation”, Adv. Math. Sci. Appl. 12 (2002) 393–408.Google Scholar
[3]Ikota, R., Ishimura, N. and Yamaguchi, T., “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.CrossRefGoogle Scholar
[4]Meron, E., “Pattern formation in excitable media”, Phys. Reports (Review Section of Phys. Lett.) 218 (1992) 1–66.Google Scholar
[5]Mikhailov, A. S., Davydov, V. A. and Zykov, A. S., “Complex dynamics of spiral waves and motion of curves”, Physica D 70 (1994) 1–39.CrossRefGoogle Scholar