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arXiv · 2303.14873

Strong attractors for the nonclassical diffusion equation with fading memory in time-dependent spaces

Yuming Qin·Xiaoling Chen·Ke Wang
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Abstract

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}(\Omega)$. 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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Yuming Qin, Xiaoling Chen, Ke Wang. 2023-03-27. Strong attractors for the nonclassical diffusion equation with fading memory in time-dependent spaces. https://arxiv.org/abs/2303.14873

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