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arXiv · 2412.10479

Pullback attractors for nonclassical diffusion equations with a delay operator

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 nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth conditions, the delay operator $\varphi(t, u_t)$ contains some hereditary characteristics and the external force $k \in L_{l o c}^{2}\left(\mathbb{R} ; L^{2}(\Omega)\right)$. First, 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. 2024-12-13. Pullback attractors for nonclassical diffusion equations with a delay operator. https://arxiv.org/abs/2412.10479

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