A global existence theorem for two coupled semilinear diffusion equations from climate modeling

A global existence theorem for two semilinear diffusion equations is proved. The equations are coupled and the diffusion coefficients are not uniformly elliptic. They arise in the study of a simple zonally averaged climate model (See also [8, 9, 13, 14]). The sectoriality of the diffusion operator is proved with the help of a technique of F. Ali Mehmeti and S. Nicaise [2]. Some imbedding results for weighted Sobolev spaces and sign conditions for the nonlinearities allow the application of a result due to Amann [3], which proves the global result.