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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 .
Some imbedding results for weighted Sobolev spaces
and sign conditions for the nonlinearities
allow the application of a result due to Amann
, which proves the global result.