带有衰退记忆的非自治经典反应扩散方程的吸引子

当非线性项以任意阶多项式增长,且外力项仅为平移有界而非平移紧时,研究了非自治经典反应扩散方程解的长时间动力学行为.应用抽象函数理论和新的估计技术,在拓扑空间L~2(Ω)×L_μ~2(R~+;H_0~1(Ω)上,证明了一致吸引子的存在性.该结果改进和推广了Chepyzhov等(2006)和钟承奎等(2006)的相应结果.

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

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 $L^2(\Omega)\times L_\mu^2(\mathbb R^+; H_0^1(\Omega))$. The result extends and improves some results by Chepyzhov et al. (2006) and Zhong et al. (2006).