Attractor for the Non-autonomous Classical Reaction Diffusion Equations with Fading Memory

摘要

The long-time dynamical behavior of the non-autonomous classical reaction diffusion equations with fading memory is studied, when the nonlinearity adheres to polynomial growth of arbitrary order and the forcing term is only translation bounded instead of translation compact. By virtue of the contract function theory and some new estimate technique, the author prove the existence of uniform attractors in the space L~2(?) × L_μ~2(R~+;H_0~1(?)). The result extends and improves some results by Chepyzhov et al. (2006) and Zhonget al. (2006).