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Convergence of a heat flow on a Hilbert manifold

Published online by Cambridge University Press:  12 July 2007

Piotr Rybka
Piotr Rybka
Affiliation:
Institute of Applied Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland ([email protected])
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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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