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A simple proof of the slope stability theorem for energy balance climate models. (English) Zbl 0936.35027

Summary: 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.

MSC:

35B35 Stability in context of PDEs
35K99 Parabolic equations and parabolic systems
35K57 Reaction-diffusion equations
35R35 Free boundary problems for PDEs
93D15 Stabilization of systems by feedback
86A40 Glaciology
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