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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

A new result for the porous medium equation derived from the Ricci flow

Author(s): Lang-Fang Wu
Journal: Bull. Amer. Math. Soc. 28 (1993), 90-94.
MathSciNet review: 1164949
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Abstract | References | Additional information

Abstract: Given $ {\mathbb{R}^2}$, with a "good" complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on $ {\mathbb{R}^2}$ is the limiting case of the porous medium equation when m is zero. The results in the Ricci flow may therefore be interpreted as sufficient conditions on the initial data, which guarantee that the corresponding unique solution for the porous medium equation on the entire plane asymptotically behaves like a "soliton-solution".

References:

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Additional Information:

DOI: 10.1090/S0273-0979-1993-00336-7
PII: S 0273-0979(1993)00336-7
Copyright of article: Copyright 1993, American Mathematical Society




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