Determination of the insolation function in the nonlinear Sellers climate model
type: Item
instance of: scholarly article
title: Determination of the insolation function in the nonlinear Sellers climate model
zbMATH Open document ID: 1270.35283
author: Judith Vancostenoble
author: Jacques Tort
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2012-10-26T00:00:00Z
review text: This very interesting paper deals with \[ u_t-\rho_0[(1-x^2)u_x]_x=r(t)q(x)\beta(u)-\epsilon(u)\left|u\right|^3u, -1<x<1, t>0, \] subject to \(\lim_{x\to\pm 1}(1-x^2)u_x(x,t)=0\) under assumptions motivated by a Sellers-type energy balance climate model. The authors provide a framework for recovering \(q\) from a given solution \(u\) (uniqueness of an inverse problem) and establish a Lipschitz stability result. To this end, they first derive global existence and uniqueness of regular solutions for the initial-boundary value problem. Key tools of the proof of the Lipschitz stability result are Carleman estimates and Hardy inequalities.
reviewed by: Georg Hetzer
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35Q86
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 6099203
zbMATH Keywords: Sellers-type climate model
zbMATH Keywords: Carleman estimates
zbMATH Keywords: Hardy inequalities
MaRDI profile type: Publication
full work available at URL: j.anihpc.2012.03.003
OpenAlex ID: W2117376531
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DOI: 10.1016/J.ANIHPC.2012.03.003
description: scientific article; zbMATH DE number 6099203