不定常空间中具有衰减记忆的非经典扩散方程的强吸引子
Strong attractors for the nonclassical diffusion equation with fading memory in time-dependent spaces
摘要：
本文讨论了具有衰减记忆的非经典扩散方程在非线性项$f$满足任意阶多项式增长和外力$ g(x)\in L^{2}(Ω)$作用下解的长时间行为.在不定常空间的框架下，利用Galerkin方法证明了强解的存在唯一性，进而得到了$\mathcal{M}_t^1$中不定常整体吸引子$\mathscr{A}=\{A_t\}_{t\in \mathbb{R}}$的存在性.
英文摘要：
In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term $f$ fulfills the polynomial growth of arbitrary order and the external force $ g(x)\in L^{2}(Ω)$. In the framework of time-dependent spaces, we verify the existence and uniqueness of strong solutions by the Galerkin method, then we obtain the existence of the time-dependent global attractor $\mathscr{A}=\{A_t\}_{t\in \mathbb{R}}$ in $\mathcal{M}_t^1$.
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