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


Hess, Peter; Poláčik, P (1994). Symmetry and convergence properties for non-negative solutions of nonautonomous reaction–diffusion problems. Proceedings of the Royal Society of Edinburgh: Section A, 124(03):573-587.

Abstract

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

Abstract

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

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Language:English
Date:1 January 1994
Deposited On:11 Oct 2018 13:53
Last Modified:27 Apr 2019 23:20
Publisher:Royal Society of Edinburgh
ISSN:0308-2105
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s030821050002878x
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S030821050002878X (Library Catalogue)

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