Determination of the insolation function in the nonlinear Sellers climate model (Q713197)

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.