Electron. J. Diff. Eqns. Vol. 1996(1996), No. 05, pp. 1-16.

Global Existence, Uniqueness, and Continuous Dependence for a Reaction-Diffusion Equation with Memory

Georg Hetzer

Global existence, uniqueness and continuous dependence on initial data are established for a quasilinear functional reaction-diffusion equation which arises from a two-dimensional energy balance climate model. Our approach relies heavily on the so-called stability estimates for linear evolution equations of parabolic type (cf. [6]).

Submitted March 17, 1996. Published July 23, 1996.
Math Subject Classification: 35K57, 34K30, 47H20, 58G11, 86A10.
Key Words: reaction-diffusion equations, memory, energy balance climate models, quasilinear parabolic functional evolution equations.

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Georg Hetzer
Department of Mathematics, 304 Parker Hall, Auburn University, AL 36849-5310, USA
e-mail: hetzege@mail.auburn.edu
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