Shen, Samuel; North, Gerald A simple proof of the slope stability theorem for energy balance climate models. (English) Zbl 0936.35027 Can. Appl. Math. Q. 7, No. 2, 203-215 (1999). 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 Keywords:linear stability; climate change; interfacial free boundary value problem; feedback reaction diffusion equation; turning point bifurcation PDFBibTeX XMLCite \textit{S. Shen} and \textit{G. North}, Can. Appl. Math. Q. 7, No. 2, 203--215 (1999; Zbl 0936.35027)