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Symmetry and convergence properties for non-negative solutions of nonautonomous reaction–diffusion problems

Published online by Cambridge University Press:  14 November 2011

Peter Hess  and
P. Poláčik
Peter Hess
Affiliation:
Mathematisches Institut, Universität Zurich, Rämistrasse 74, 8001 Züurich, Switzerland
P. Poláčik
Affiliation:
Institute of Applied Mathematics, Comenius University, Mlynská Dolina, 824 15 Bratislava, Slovakia
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Abstract

Nonautonomous parabolic equations of the form ut − Δu = f(u, t) on a symmetric domain are considered. Using the moving-hyperplane method, it is proved that any bounded nonnegative solution symmetrises as t → ∞. This is then used to show that for nonlinearities periodic in t, any non-negative bounded solution approaches a periodic solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 3 , 1994 , pp. 573 - 587
Copyright
Copyright © Royal Society of Edinburgh 1994

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