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A comparison theorem for solutions of degenerate parabolic equations on manifolds

Published online by Cambridge University Press:  28 July 2008

S. A. J. Dekkers
S. A. J. Dekkers
Affiliation:
Mathematisch Instituut, Utrecht University, Postbus 80010, 3508 TA Utrecht, The Netherlands ([email protected])
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Abstract

We compare solutions of a class of degenerate parabolic equations on a Riemannian manifold $M$ with solutions of the equation on a model manifold. The class of equations under consideration contains both the parabolic $p$-Laplace equation and the porous medium equation. We prove that, under curvature conditions, solutions on model manifolds induce sub- or supersolutions on $M$. Using this result, we obtain curvature-dependent estimates for the speed of propagation of solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 4 , August 2008 , pp. 755 - 767
Copyright
2008 Royal Society of Edinburgh

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