带衰退记忆的非自治非经典扩散方程的吸引子

Attractors for the non-autonomous nonclassical diffusion equation with fading memory

在空间H^(1)_(0)(Ω)×L^(2)_(μ)(R^(+);H^(1)_(0)(Ω))中,当非线性项f(u,t)次临界增长时,讨论了具有衰退记忆的非自治非经典扩散方程解的长时间动力学行为。当外力项仅满足平移有界而非平移紧时,通过渐近正则估计技术,得到了紧一致吸引子的存在性及其拓扑结构。

The long-time dynamical behavior of solutions for the non-autonomous nonclassical diffusion equation with fading memory and subcritical nonlinearity is discussed in the space H^(1)_(0)(Ω)×L^(2)_(μ)(R^(+);H^(1)_(0)(Ω)).When the external term g(x,t)is only translation bounded instead of translation compact,by means of the asymptotic regularity estimate technique,the existence and topological structure of a compact uniform attractor is obtained.