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arXiv · 2307.15789

Existence and regularity of pullback attractors for nonclassical non-autonomous diffusion equations with delay

Bin Yang·Yuming Qin·Alain Miranville·Ke Wang
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Abstract

In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some hereditary characteristics and the external force $h \in L_{l o c}^{2}\left(\mathbb{R} ; L^{2}(\Omega)\right)$. Firstly, we prove the well-posedness of solutions by using the Faedo-Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time-dependent spaces $C_{\mathcal{H}_{t}(\Omega)}$ and $C_{\mathcal{H}^{1}_{t}(\Omega)}$ respectively.

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Bin Yang, Yuming Qin, Alain Miranville, Ke Wang. 2023-07-28. Existence and regularity of pullback attractors for nonclassical non-autonomous diffusion equations with delay. https://arxiv.org/abs/2307.15789

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