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October  1997, 3(4): 541-564. doi: 10.3934/dcds.1997.3.541

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

Olaf Hansen 1,

1. 

Department of Mathematics, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany

Received  June 1996 Published  July 1997

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.
Keywords: Nonlinear parabolic equations, coupled system, climate modeling., spectral theory.
Mathematics Subject Classification: 35K15, 35K55, 35P0.
Citation: Olaf Hansen. A global existence theorem for two coupled semilinear diffusion equations from climate modeling. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 541-564. doi: 10.3934/dcds.1997.3.541
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