On a two-point free boundary problem

Authors:
Jong-Shenq Guo and Bei Hu

Journal:
Quart. Appl. Math. **64** (2006), 413-431

MSC (2000):
Primary 35K20, 35K55

DOI:
https://doi.org/10.1090/S0033-569X-06-01021-1

Published electronically:
June 12, 2006

MathSciNet review:
2259046

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Abstract: We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straight lines. Depending on these two touching angles, there are three different cases, namely, area-expanding, area-preserving, and area-shrinking cases. We first give a proof of the global existence in the expanding and preserving cases. Then the convergence to a line in the preserving case is derived. Finally, in the shrinking case, we show the finite-time vanishing and the convergence of the solution to a self-similar solution.

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Additional Information

**Jong-Shenq Guo**

Affiliation:
Department of Mathematics, National Taiwan Normal University, S-4 Ting Chou Road, Taipei 117, Taiwan

Email:
jsguo@math.ntnu.edu.tw

**Bei Hu**

Affiliation:
Department of Mathematics, University of Notre Dame, Room 255, Hurley, Notre Dame, Indiana 46556

Email:
b1hu@nd.edu

DOI:
https://doi.org/10.1090/S0033-569X-06-01021-1

Received by editor(s):
January 18, 2005

Published electronically:
June 12, 2006

Article copyright:
© Copyright 2006
Brown University

The copyright for this article reverts to public domain 28 years after publication.