Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-27T11:34:45.244Z Has data issue: false hasContentIssue false

An ordinary differential equation arising in the Ricci flow on the plane

Published online by Cambridge University Press:  17 February 2009

Jong-Shenq Guo
Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, Sec. 4, Ting-Chou Road, Taipei 117, Taiwan. E-mail addresses: jsguo@math.ntnu.edu.tw and yjguo@math.ntnu.edu.tw.
Yung-Jen Lin Guo
Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, Sec. 4, Ting-Chou Road, Taipei 117, Taiwan. E-mail addresses: jsguo@math.ntnu.edu.tw and yjguo@math.ntnu.edu.tw.
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 consider an ordinary differential equation arising in the study of the Ricci flow on R2. The existence and uniqueness of solutions of this equation are derived. We then study the asymptotic behaviour of these solutions at ±∞.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1] Daskalopoulos, P. and del Pino, M. A., “On fast diffusion nonlinear heat equations and a related singular elliptic problem”, Indiana Univ. Math. J. 43 (1994) 703728.CrossRefGoogle Scholar
[2] Daskalopoulos, P. and del Pino, M. A., “On a singular diffusion equation”, Comm. Anal. Geom. 3 (1995) 523542.CrossRefGoogle Scholar
[3] Davis, S. H., DiBenedetto, E. and Diller, D. J., “Some a priori estimates for a singular evolution equation arising in thin-film dynamics”, SIAM J. Math. Anal. 27 (1996) 638660.CrossRefGoogle Scholar
[4] DiBenedetto, E. and Diller, D. J., About a singular parabolic equation arising in thin film dynamics and in the Ricci flow for complete R2, Lecture Notes on Pure and Applied Math. vol. 177 (1996) 103120.Google Scholar
[5] Guo, J.-S., “On the Cauchy problem for a very fast diffusion equation”, Comm. P.D.E. 21 (1996) 13491365.Google Scholar
[6] Hamilton, R., The Ricci flow on surfaces, Contemp. Math. vol. 71 (Amer. Math. Soc., Providence, RI, 1988) 237262.Google Scholar
[7] Vazquez, J. L., “Nonexistence of solutions for nonlinear heat equations of fast-diffusion type”, J. Math. Pure Appl. 71 (1992) 503526.Google Scholar
[8] Vazquez, J. L., Esteban, J. R. and Rodriguez, A., “The fast diffusion equation with logarithmic nonlinearity and the evolution of conformal metrics in the plane”. Advances in Differential Equations 1 (1996) 2150.Google Scholar
[9] Wu, L.-F., “The Ricci flow on complete R2”, Comm. Anal. Geom. 1 (1993) 437472.CrossRefGoogle Scholar