Articles | Volume 31, issue 1
Research article
08 Mar 2024
Research article |  | 08 Mar 2024

Variational techniques for a one-dimensional energy balance model

Gianmarco Del Sarto, Jochen Bröcker, Franco Flandoli, and Tobias Kuna

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Subject: Bifurcation, dynamical systems, chaos, phase transition, nonlinear waves, pattern formation | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

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Baldi, P.: Stochastic Calculus, Springer International Publishing,, 2017. a
Bastiaansen, R., Dijkstra, H. A., and von der Heydt, A. S.: Fragmented tipping in a spatially heterogeneous world, Environ. Res. Lett., 17, 045006,, 2022. a, b, c, d, e, f, g
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Brezis, H.: Functional analysis, Sobolev spaces and partial differential equations, vol. 2, Springer,, 2011.Please provide persistent identifier (DOI preferred). a, b
Short summary
We consider a one-dimensional model for the Earth's temperature. We give sufficient conditions to admit three asymptotic solutions. We connect the value function (minimum value of an objective function depending on the greenhouse gas (GHG) concentration) to the global mean temperature. Then, we show that the global mean temperature is the derivative of the value function and that it is non-decreasing with respect to GHG concentration.