Volume 7, Number 2, Summer 1999
A SIMPLE PROOF OF THE
SLOPE STABILITY THEOREM FOR
ENERGY BALANCE CLIMATE MODELS
SAMUEL SHEN AND GERALD NORTH
Abstract. In this paper a simple proof of the slope
stability theorem for energy balance climate models is given.
Mathematically, this is an interfacial free boundary value
problem of a feedback reaction diffusion equation. The subtle
technique of implicit differentiation in studying the stability
of a regular turning point bifurcation problem is utilized and
makes the proof of the slope stability theorem simpler than
the existing proofs. The proof method and the derived results
are useful in studying the sensitivity of the global climate to
external forcings.
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