School of Mathematics
University of Minnesota
eta vs A


Nonsmooth frameworks for an extended Budyko model

Anna M. Barry, Esther Widiasih, and Richard McGehee

Discrete & Continuous Dynamical Systems Series B 22 (2017) (6), 2447-2463. doi: 10.3934/dcdsb.2017125


Abstract.  In latitude-dependent energy balance models, ice-free and ice-covered conditions form physical boundaries of the system. With carbon dioxide treated as a bifurcation parameter, the resulting bifurcation diagram is nonsmooth with curves of equilibria and boundaries forming corners at points of intersection. Over long time scales, atmospheric carbon dioxide varies dynamically and the nonsmooth diagram becomes a set of quasi-equilibria. However, when introducing carbon dynamics, care must be taken with the physical boundaries and appropriate boundary motion specified. In this article, we extend an energy balance model to include slowly varying carbon dioxide and develop nonsmooth frameworks based on physically relevant boundary dynamics. Within these frameworks, we prove existence and uniqueness of solutions, as well as invariance of the region of phase space bounded by ice-free and ice-covered states.

Electronic Copies

The paper is available for subscribers on the publisher's Web site:
doi: 10.3934/dcdsb.2017125

December 14, 2017, version:
ArXiv: arXiv:1406.6028
Cached Copy: Barry2017ArXiv-v3.pdf

13 October 2015 version:
ArXiv: arXiv:1406.6028v2
Cached Copy: Barry2017ArXiv-v2.pdf

23 June 2014 version:
ArXiv: arXiv:1406.6028v1
Cached copy: Barry2017ArXiv-v1.pdf


Last update: May 12, 2018 ©2018 Richard McGehee