具有时间依赖记忆核的非经典扩散方程的吸引子

Attractors for the Nonclassical Diffusion Equation with Time-Dependent Memory Kernel

该文在时间依赖空间H_(0)^(1)(Ω)×L_(μt)^(2)(R^(+);H_(0)^(1)(Ω))中研究了具有时间依赖记忆核的非经典扩散方程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得到了解的适定性,进而证明了时间依赖全局吸引子的存在性与正则性.

In this paper,we study the long-time dynamical behavior of solutions for the nonclassical diffusion equation with time-dependent memory kernel in the time-dependent space H_(0)^(1)(Ω)×L_(μt)^(2)(R^(+);H_(0)^(1)(Ω)).Under the new theorical framework,the well-posedness of the solution,the existence and the regularity of the time-dependent global attractors are proved by using the delicate integral estimation method and decomposition technique.