Global Attractors for the Classical Reaction Diffusion Equations with Fading Memory

摘要

The authors study the long-time dynamical behavior of the classical reaction diffusion equations with fading memory, when the nonlinearity adheres to polynomial growth of arbitrary order and the forcing term belongs only to H-1(Ω). By virtue of the contract function theory, semigroup theory and some new estimate technique, the authors prove the existence of global attractors in the space L~2(Ω) × H_0~1(Ω)). The result extends and improves some results by Chepyzhov et al. (2006) and Zhong et al. (2006).