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Gradient-like parabolic semiflows on BUC(ℝN)

Published online by Cambridge University Press:  14 November 2011

Daniel Daners  and
Sandro Merino
Daniel Daners
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia e-mail: daners@maths.usyd.edu.au
Sandro Merino
Affiliation:
Mathematisches Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland e-mail: merino@math.unizh.ch
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Extract

We prove that a class of weighted semilinear reaction diffusion equations on RN generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on RN. If N = 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1281 - 1291
Copyright
Copyright © Royal Society of Edinburgh 1998

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