具有时间依赖记忆核的粘弹性方程的吸引子

Attractors for the Viscoelastic Equationwith Time-Dependent Memory Kernel

对于具有时间依赖记忆核的粘弹性方程,本文研究了该方程解的长时间动力学行为。 当非线性项 f 的增长指数 p 满足1≤p≤5时,在新的理论框架下,利用积分估计方法得到了解的适定性。 同时,当 p 满足1≤p<5时,证明了时间依赖全局吸引子的存在性以及不变性。

In this paper, we investigate the long-time dynamical behavior of solutions for the viscoelastic equation with time-dependent memory kernel. When the growth exponent p of nonlinearity f(u) is up to 1≤p≤5, the well-posedness of the solutions is proved by using the integral estimation method, and we obtained an invariant time-dependent global attractor when 1≤p<5 .