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1995 A functional reaction-diffusion equation from climate modeling: S-shapedness of the principal branch of fixed points of the time-$1$-map
Georg Hetzer
Differential Integral Equations 8(5): 1047-1059 (1995).

Abstract

If the seasonal cycle as well as the long response times of the climate system are taken into account, one-layer energy balance climate models give rise to parameter-dependent functional reaction-diffusion equations with 1-periodic forcing and a time delay $T\gg 1$. We show that the principal branch of fixed points of the corresponding time-1-map is S-shaped in the sense that it is a simple curve with an even number of turning points. This curve connects $(0,\mathbf {0})$ and $(\infty , \infty )$ within $(0,\infty) \times C([-T,0]\times M,(0,\infty))$, $M$ a compact, oriented Riemannian surface. The paper is a continuation of [13], where a case without time-delay was considered.

Citation

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Georg Hetzer. "A functional reaction-diffusion equation from climate modeling: S-shapedness of the principal branch of fixed points of the time-$1$-map." Differential Integral Equations 8 (5) 1047 - 1059, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0822.35069
MathSciNet: MR1325545

Subjects:
Primary: 35R10
Secondary: 35B32, 35K57, 47H15, 47N20, 58F39, 86A10

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.8 • No. 5 • 1995
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