Global solutions to norm-preserving non-local flows of porous media type
Published online by Cambridge University Press: 17 July 2013
Abstract
In this paper, we study the global existence of positive solutions to the norm-preserving non-local heat flow of the porous-media type equations on the compact Riemannian manifold (M, g) with the Cauchy data u0 > 0 on M, where r ≥ 1, p > 1 and λ(t) is chosen to make the L2-norm of the solution u (or a power of u) constant. We show that the limit is an eigenfunction for the Laplacian operator. We use some tricky estimates through the Sobolev imbedding theorem and the Moser iteration method.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 4 , August 2013 , pp. 871 - 880
- Copyright
- Copyright © Royal Society of Edinburgh 2013
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