【摘要】 关于具有时间依赖记忆核的经典反应扩散方程,当非线性项满足次临界增长,外力项g（x,t）∈L_loc²（R;L²（?））时,在时间依赖空间L²（?）×L_μt²（R₊;H₀¹（?））中讨论了解的长时间动力学行为.在新的理论框架下,利用积分估计方法以及分解技术证明了解的适定性和正则性,进而证明了时间依赖拉回吸引子的存在性.更多还原

【Abstract】 This paper presents a discussion on the long-time dynamical behavior of solutions for the classical reaction-diffusion equation with time-dependent memory kernel when nonlinear term adheres to subcritical growth and the external force term g（x,t） belongs to the space L_loc²（R;L²（?））in the time-dependent space L²（?）×L_μt²（R₊;H₀¹（?））.Within the new theorical framework,the well-posedness and the regularity of the solution,as well as the existence of the time-dependent pullback attractors are established.This is achieved by applying the delicate integral estimation method and decomposition techniques.更多还原