Differential and Integral Equations

A functional reaction-diffusion equation from climate modeling: S-shapedness of the principal branch of fixed points of the time-$1$-map

Georg Hetzer

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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.

Article information

Source
Differential Integral Equations, Volume 8, Number 5 (1995), 1047-1059.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056043

Mathematical Reviews number (MathSciNet)
MR1325545

Zentralblatt MATH identifier
0822.35069

Subjects
Primary: 35R10: Partial functional-differential equations
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35K57: Reaction-diffusion equations 47H15 47N20: Applications to differential and integral equations 58F39 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]

Citation

Hetzer, Georg. 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 (1995), no. 5, 1047--1059. https://projecteuclid.org/euclid.die/1369056043


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