## Mathematical analysis of some diffusive energy balance models in climatology.(English)Zbl 0804.92026

Diaz, J.-I. (ed.) et al., Mathematics, climate and environment. Paris: Masson. Res. Notes Appl. Math. 27, 28-56 (1993).
The paper is devoted to the study of the nonlinear parabolic problem $u_ t - (\rho (x) | u_ x |^{p - 2} u_ x)_ x = R_ a (x,t,u) - R_ e (x,t,u), \quad x \in I,\;t>0,$
$\rho (x) \cdot | u_ x |^{p - 2} u_ x = 0,\;x \in \partial I,\;t>0, \qquad u (x,0) = u_ 0 (x),\;x \in I = ( - 1,1).$ The problem arises from climate modelling, more specifically from an energy climate model due to Held and Suarez (1974) where the case $$p=3$$ was proposed. Many of the results obtained for $$p=3$$ are obtained in this work under the general assumption $$1 < p < + \infty$$. There are also applications to the classical models introduced by M. I. Budyko [Tellus 21, 611-619 (1969)] and W. D. Sellers [Geofis. Int. 14, 303-315 (1969)].
For the entire collection see [Zbl 0782.00023].

### MSC:

 92D40 Ecology 35K55 Nonlinear parabolic equations 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92D99 Genetics and population dynamics

### Keywords:

climate modelling; energy climate model