A functional reaction-diffusion equation from climate modeling: \(S\)- shapedness of the principal branch of fixed points of the time-1-map. (English) Zbl 0822.35069

Hetzer, Georg

Differ. Integral Equ. 8, No. 5, 1047-1059 (1995).

Summary: 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 \((0,0)\) and \((\infty, \infty)\) within \((0,\infty) \times C([-T, 0]\times M, (0, \infty))\), \(M\) a compact, oriented Riemannian surface.

MSC:

35K57	Reaction-diffusion equations
35R10	Partial functional-differential equations
86A10	Meteorology and atmospheric physics

Keywords:

climate models