Convergence of a heat flow on a Hilbert manifold
Published online by Cambridge University Press: 12 July 2007
Abstract
We study the heat flow projected on a manifold M ⊂ L2(Ω). This manifold is defined by the condition that the integrals ∫Ωuk (t,x) dx, k = 1,…,N, are constants of motion. We show that solutions to this problem converge to a steady state as time tends to +∞. We use in an essential way a variant of the Łojasiewicz inequality.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 4 , August 2006 , pp. 851 - 862
- Copyright
- Copyright © Royal Society of Edinburgh 2006
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